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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Physiol.</journal-id>
<journal-title>Frontiers in Physiology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Physiol.</abbrev-journal-title>
<issn pub-type="epub">1664-042X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
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<article-meta>
<article-id pub-id-type="publisher-id">1612900</article-id>
<article-id pub-id-type="doi">10.3389/fphys.2025.1612900</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physiology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Leveraging artificial intelligence for early detection and prediction of acute kidney injury in clinical practice</article-title>
<alt-title alt-title-type="left-running-head">Liang et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphys.2025.1612900">10.3389/fphys.2025.1612900</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Liang</surname>
<given-names>Bo</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<role content-type="https://credit.niso.org/contributor-roles/Conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/Methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/Software/"/>
<role content-type="https://credit.niso.org/contributor-roles/Data curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/Formal analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/Project administration/"/>
<role content-type="https://credit.niso.org/contributor-roles/Investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Funding acquisition/"/>
<role content-type="https://credit.niso.org/contributor-roles/Resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/Visualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/Validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - original draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing - review and editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ma</surname>
<given-names>Congsha</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/Formal analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/Investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Data curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - original draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review and editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Lei</surname>
<given-names>Ming</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3038108/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
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<role content-type="https://credit.niso.org/contributor-roles/Funding acquisition/"/>
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</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Internal Medicine</institution>, <institution>Xinxiang Central Hospital</institution>, <institution>The Fourth Clinical College of Xinxiang Medical University</institution>, <addr-line>Xinxiang</addr-line>, <addr-line>Henan</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Department of Education</institution>, <institution>School of Nursing and Health</institution>, <institution>Shanghai Zhongqiao Vocational and Technical University</institution>, <addr-line>Shanghai</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Department of Education</institution>, <institution>School of Nursing</institution>, <institution>Shanghai Lida University</institution>, <addr-line>Shanghai</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2184974/overview">Miodrag Zivkovic</ext-link>, Singidunum University, Serbia</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2816460/overview">Navya Prakash</ext-link>, Carl von Ossietzky University of Oldenburg, Germany</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2838956/overview">Celeste Dixon</ext-link>, Children&#x2019;s Hospital of Philadelphia, United States</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Bo Liang, <email>doubadgoolap@hotmail.com</email> </corresp>
</author-notes>
<pub-date pub-type="epub">
<day>24</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>16</volume>
<elocation-id>1612900</elocation-id>
<history>
<date date-type="received">
<day>19</day>
<month>04</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>15</day>
<month>07</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Liang, Ma and Lei.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Liang, Ma and Lei</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>Acute kidney injury (AKI) is a severe and rapidly developing condition characterized by a sudden deterioration in renal function, impairing the kidneys&#x2019; ability to excrete metabolic waste and regulate fluid balance. Timely detection of AKI poses a significant challenge, largely due to the reliance on retrospective biomarkers such as elevated serum creatinine, which often manifest after substantial physiological damage has occurred. The deployment of AI technologies in healthcare has advanced early diagnostic capabilities for AKI, supported by the predictive power of modern machine learning frameworks. Nevertheless, many traditional approaches struggle to effectively model the temporal dynamics and evolving nature of kidney impairment, limiting their capacity to deliver accurate early predictions.</p>
</sec>
<sec>
<title>Methods</title>
<p>To overcome these challenges, we propose an innovative framework that fuses static clinical variables with temporally evolving patient information through a Long Short-Term Memory (LSTM)-based deep learning architecture. This model is specifically designed to learn the progression patterns of kidney injury from sequential clinical data&#x2014;such as serum creatinine trajectories, urine output, and blood pressure readings. To further enhance the model&#x2019;s temporal sensitivity, we incorporate an attention mechanism into the LSTM structure, allowing the network to prioritize critical time segments that carry higher predictive value for AKI onset.</p>
</sec>
<sec>
<title>Results</title>
<p>Empirical evaluations confirm that our approach surpasses conventional prediction methods, offering improved accuracy and earlier detection.</p>
</sec>
<sec>
<title>Discussion</title>
<p>This makes it a valuable tool for enabling proactive clinical interventions. The proposed model contributes to the expanding landscape of AI-enabled healthcare solutions for AKI, supporting the broader initiative to incorporate intelligent systems into clinical workflows to improve patient care and outcomes.</p>
</sec>
</abstract>
<kwd-group>
<kwd>acute kidney injury</kwd>
<kwd>artificial intelligence</kwd>
<kwd>early detection</kwd>
<kwd>machine learning</kwd>
<kwd>temporal prediction</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Computational Physiology and Medicine</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Acute Kidney Injury (AKI) is a major clinical challenge, primarily due to its strong association with increased morbidity and mortality <xref ref-type="bibr" rid="B36">Wei et al. (2022)</xref>. Early identification of AKI is essential for enabling timely medical intervention, which may mitigate disease progression and significantly improve patient outcomes <xref ref-type="bibr" rid="B30">Stubnya et al. (2024a)</xref>. However, detecting AKI at an early stage remains difficult, as initial symptoms are often vague and clinically ambiguous <xref ref-type="bibr" rid="B19">Malhotra et al. (2017)</xref>. Common diagnostic tools, such as monitoring serum creatinine and urine output, frequently fail to recognize the onset of AKI until substantial kidney damage has occurred <xref ref-type="bibr" rid="B7">Dong et al. (2021)</xref>. Given the rapid progression and multifactorial nature of AKI, there is a growing demand for advanced computational approaches that can provide accurate predictions and real-time clinical support <xref ref-type="bibr" rid="B8">Fletchet et al. (2018)</xref>.</p>
<p>Early technological attempts to assist AKI detection were anchored in structured frameworks that relied heavily on fixed diagnostic guidelines and rule-based clinical logic <xref ref-type="bibr" rid="B14">Hu et al. (2016)</xref>. Systems were developed to simulate clinical decision processes by aligning patient metrics with predefined thresholds or logical criteria <xref ref-type="bibr" rid="B34">Tseng et al. (2020)</xref>. For instance, decision pathways based on combinations of vital signs and lab indicators were used to flag abnormal renal function <xref ref-type="bibr" rid="B9">Gameiro et al. (2021)</xref>. While these methods offered interpretability and alignment with clinical expertise, they were often rigid, failing to capture patient-specific nuances or adapt to complex physiological variations <xref ref-type="bibr" rid="B29">Song et al. (2021)</xref>. Their limited scalability and lack of flexibility across diverse healthcare settings hindered broad clinical application <xref ref-type="bibr" rid="B33">Toma&#x161;ev et al. (2019)</xref>.</p>
<p>To address these limitations, researchers introduced algorithmic approaches capable of learning associations from empirical patient records <xref ref-type="bibr" rid="B31">Stubnya et al. (2024b)</xref>. Instead of relying solely on fixed medical logic, newer models began identifying risk signatures using patterns derived from clinical variables such as lab values, comorbidities, and hemodynamic profiles <xref ref-type="bibr" rid="B18">Li et al. (2018)</xref>. Predictive models like support vector machines and ensemble classifiers were employed to stratify AKI risk more accurately and efficiently <xref ref-type="bibr" rid="B32">Tan et al. (2024)</xref>. Although these techniques improved detection performance and enabled broader generalization, they struggled with unstructured data and often lacked transparency in how predictions were derived <xref ref-type="bibr" rid="B1">Abbas et al. (2024)</xref>. Additionally, their dependency on high-quality labeled data restricted applicability in real-time clinical workflows <xref ref-type="bibr" rid="B5">Bihorac et al. (2018)</xref>.</p>
<p>Recent advancements in AI research have ushered in a new wave of models that learn directly from complex, multimodal data sources with minimal manual intervention <xref ref-type="bibr" rid="B10">Gogoi and Valan (2025)</xref>. Deep learning architectures such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are increasingly used to analyze rich clinical datasets <xref ref-type="bibr" rid="B35">Wang et al. (2019)</xref>. Furthermore, pre-trained models including transformer-based networks are being adapted to healthcare applications, showing great promise in forecasting AKI events from diverse data inputs such as clinical notes, lab trends, and medical imaging <xref ref-type="bibr" rid="B6">Churpek et al. (2019)</xref>. These systems often outperform earlier techniques in both accuracy and scalability, especially in large-scale hospital environments <xref ref-type="bibr" rid="B13">Hirsch (2020)</xref>. However, the complexity of their inner workings poses a challenge for clinical adoption, reinforcing the urgent need for interpretable AI frameworks that can provide clinicians with both accurate predictions and actionable explanations <xref ref-type="bibr" rid="B11">Gottlieb et al. (2022)</xref>. In our framework, symbolic AI refers to the use of logic-based methods that represent expert knowledge in a structured, rule-driven format <xref ref-type="bibr" rid="B22">Parikh et al. (2011)</xref>. Unlike data-driven models, symbolic AI systems rely on human-defined ontologies, decision rules, or knowledge graphs to model relationships between clinical variables <xref ref-type="bibr" rid="B7">Dong et al. (2021)</xref>. In the context of our work, symbolic AI is used to encode medical domain knowledge&#x2014;for instance, established clinical criteria for AKI diagnosis or known physiological dependencies&#x2014;into machine-readable logic structures <xref ref-type="bibr" rid="B32">Tan et al. (2024)</xref>. These symbolic components are integrated with machine learning and deep learning layers to enhance interpretability and support reasoning under limited data conditions <xref ref-type="bibr" rid="B42">Zhang et al. (2024)</xref>.</p>
<p>Recent advances in artificial intelligence have demonstrated promising results in medical diagnostics, particularly in early detection of acute conditions such as AKI <xref ref-type="bibr" rid="B2">Alfieri et al. (2023)</xref>. Supervised learning models trained on large clinical datasets have enabled the identification of complex, nonlinear patterns that may precede physiological deterioration <xref ref-type="bibr" rid="B15">Huang et al. (2023)</xref>. These models, leveraging variables such as serum creatinine, urine output, and blood pressure, can assist clinicians by providing early warning signals and supporting timely interventions <xref ref-type="bibr" rid="B25">Rank et al. (2020)</xref>. However, challenges remain in real-world clinical deployment, including handling heterogeneous data formats from EHRs, managing missing values, and ensuring model interpretability <xref ref-type="bibr" rid="B20">Martinez et al. (2020)</xref>. Moreover, ethical concerns regarding transparency, accountability, and data privacy necessitate careful design and validation of AI systems before clinical adoption <xref ref-type="bibr" rid="B20">Martinez et al. (2020)</xref>. To address these limitations, our approach integrates symbolic AI with deep temporal models, allowing the system to incorporate expert-defined clinical logic while learning from patient-specific temporal patterns <xref ref-type="bibr" rid="B38">Xu et al. (2024)</xref>. This hybrid framework improves both the predictive power and explainability of the system, supporting robust decision-making in dynamic and data-sparse environments <xref ref-type="bibr" rid="B27">Shang et al. (2020)</xref>.</p>
<p>Although recent advances in AI-based techniques have improved acute kidney injury (AKI) detection, substantial challenges remain, highlighting the need for more robust and effective solutions <xref ref-type="bibr" rid="B28">Shang and Yao (2014)</xref>. Traditional approaches, as previously outlined, are constrained by their limited capacity to process high-dimensional <xref ref-type="bibr" rid="B26">Shang et al. (2010)</xref>, heterogeneous data and their dependence on fixed rules or annotated datasets <xref ref-type="bibr" rid="B40">Yu et al. (2024)</xref>. While machine learning has mitigated some of these constraints, issues related to model interpretability and generalization persist <xref ref-type="bibr" rid="B37">Xie et al. (2025)</xref>. Although deep learning techniques are effective in capturing complex data patterns, their limited transparency and explainability remain challenges in clinical applications <xref ref-type="bibr" rid="B16">Huang (2025)</xref>.</p>
<p>To overcome these challenges, we propose an innovative AI-powered framework that integrates traditional techniques with modern approaches in a cohesive manner. Our proposed system incorporates symbolic AI to encode structured domain knowledge, machine learning algorithms to uncover patterns from data, and deep learning models to capture intricate temporal and nonlinear relationships. This hybrid strategy not only elevates prediction performance but also promotes interpretability and reliability, thereby enhancing the model&#x2019;s applicability in real-world healthcare environments.</p>
<p>Kidney injury, often referred to as acute kidney injury (AKI), is a common and serious clinical condition characterized by a sudden decrease in kidney function. This impairment leads to an inability of the kidneys to filter waste, balance fluid and electrolyte levels, and regulate blood pressure, which can result in a buildup of toxins in the body. AKI can manifest in various forms, ranging from mild and reversible to severe, requiring dialysis or leading to long-term kidney damage. In <xref ref-type="sec" rid="s2-1">Section 2.1</xref>, the causes of kidney injury are multifactorial and can be classified into prerenal, intrinsic renal, and postrenal categories. Prerenal kidney injury occurs when blood flow to the kidneys is reduced, often due to conditions such as dehydration, heart failure, or blood loss. Intrinsic renal injury involves damage to the kidney tissue itself, which may result from diseases like glomerulonephritis or tubular injury caused by toxins or infections. Postrenal injury arises from obstructions in the urinary tract that hinder the outflow of urine, such as kidney stones or tumors. As detailed in <xref ref-type="sec" rid="s2-2">Section 2.2</xref>, the standard clinical identification of AKI predominantly relies on monitoring variations in serum creatinine concentration and urine output. However, these conventional biomarkers often exhibit a delayed physiological response, which can hinder timely detection and compromise the effectiveness of therapeutic intervention. Consequently, considerable research efforts have been directed toward discovering novel biomarkers and developing predictive diagnostic methods capable of identifying renal injury at an earlier stage&#x2014;prior to the onset of overt clinical symptoms. In <xref ref-type="sec" rid="s2-3">Section 2.3</xref>, the treatment of kidney injury depends on the underlying cause, with strategies ranging from fluid resuscitation in prerenal cases to the use of medications or dialysis for severe intrinsic renal or postrenal conditions. Early detection and prompt management are critical for improving patient outcomes and preventing the progression to chronic kidney disease (CKD). Recent advancements have substantially deepened the comprehension of the molecular basis of kidney injury, especially concerning processes such as inflammatory responses, oxidative damage, and programmed cell death. Emerging developments in regenerative medicine&#x2014;including stem cell-based interventions&#x2014;present encouraging prospects for therapeutic strategies targeting renal tissue restoration. This section explores the pathophysiology, diagnostic challenges, and therapeutic approaches to kidney injury, with a particular focus on emerging strategies for early detection and personalized treatment options. In the subsequent sections, we will examine specific biomarkers of kidney injury, novel therapeutic interventions, and the potential for integrating these advancements into clinical practice to enhance patient care and outcomes.</p>
</sec>
<sec sec-type="methods" id="s2">
<title>2 Methods</title>
<sec id="s2-1">
<title>2.1 Preliminaries</title>
<p>In our study, Acute Kidney Injury (AKI) was identified based on the KDIGO (Kidney Disease: Improving Global Outcomes) criteria. A patient was labeled as having AKI if any of the following conditions were met: an increase in serum creatinine (SCr) of <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mo>&#x2265;</mml:mo>
<mml:mn>0.3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> mg/dL within 48 h, an increase in SCr to <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mo>&#x2265;</mml:mo>
<mml:mn>1.5</mml:mn>
</mml:mrow>
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</inline-formula> times the baseline within the prior 7 days, or a reduction in urine output to <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>0.5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> mL/kg/h for more than 6 h. These thresholds align with widely adopted clinical diagnostic standards, ensuring consistency across datasets. For model training and prediction, we focused on clinically relevant time points within a 48-h observation window prior to the first documented AKI event. Time-series features were sampled hourly, resulting in sequences ranging from 6 to 48 time steps depending on data availability. The model was designed to make AKI risk predictions at each hourly time point, enabling dynamic monitoring of renal function. Regarding cohort construction, we included adult ICU patients (age <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:mo>&#x2265;</mml:mo>
<mml:mn>18</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>) with at least 12 consecutive hours of recorded data prior to AKI diagnosis. Patients were excluded if they had known end-stage renal disease (ESRD), a history of dialysis, missing baseline creatinine, or insufficient data (fewer than 6 recorded time steps). These inclusion and exclusion criteria ensure a robust dataset suitable for temporal modeling and reduce noise introduced by chronic kidney disease or incomplete records.</p>
<p>In real-world clinical environments, time-series data is frequently plagued by missing or irregular entries, which can pose significant challenges to deep learning-based temporal prediction systems. To address this, our workflow incorporates a two-fold strategy. We apply forward-fill and backward-fill imputation for short-term gaps in vital signs and lab measurements, followed by statistical imputation, such as mean or median values within patient-specific context, for persistent missing features. For categorical variables, missing entries are encoded with a designated embedding vector. This hybrid imputation approach is seamlessly integrated into the data preprocessing pipeline prior to model training and inference. Our LSTM-based model is designed to accommodate variable-length sequences without strict requirements on the minimum number of time steps. During training, variable-length sequences are padded with masking to ensure consistent batch sizes, and masked positions are ignored during loss computation.</p>
<p>Kidney injury is a complex and multifactorial condition that can arise from various etiological factors. To formally define and understand the problem of kidney injury, we start by introducing some key concepts and mathematical formulations relevant to the diagnosis and treatment strategies. These preliminaries will lay the foundation for the development of a model to better predict and manage kidney injury.</p>
<p>Let <inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> denote the matrix of clinical observations, where <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> corresponds to the total number of patients and <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the number of clinical attributes per individual. Each feature dimension may represent variables such as blood pressure, serum creatinine concentration, urine output, and other relevant physiological indicators. The central objective is to learn a functional mapping from the input space <inline-formula id="inf8">
<mml:math id="m8">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> to a continuous or discrete estimation reflecting the severity of acute kidney injury in each patient (<xref ref-type="disp-formula" rid="e1">Equation 1</xref>).<disp-formula id="e1">
<mml:math id="m9">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
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</mml:mrow>
<mml:mo>&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>f</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
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</mml:mrow>
</mml:msub>
<mml:mo>;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> represents the model parameters, which are learned from historical data.</p>
<p>A critical component in predicting kidney injury is the analysis of biomarkers that correlate with kidney function. Let <inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
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</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
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</mml:mrow>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> be a binary indicator of kidney injury for patient <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf12">
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<mml:mrow>
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</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> indicates the presence of kidney injury, and <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> indicates no injury. The core goal of the model involves optimizing predictions by minimizing their inconsistency with the true labels through the binary cross-entropy criterion (<xref ref-type="disp-formula" rid="e2">Equation 2</xref>).<disp-formula id="e2">
<mml:math id="m15">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo>&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mo>&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>Recent studies have identified various biomarkers and physiological variables that might help improve the model&#x2019;s predictive power. These biomarkers, denoted by <inline-formula id="inf14">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, are included as additional features in the dataset <inline-formula id="inf15">
<mml:math id="m17">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and their relationships with kidney injury outcomes need to be explored. The biomarkers <inline-formula id="inf16">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> refer to clinically validated variables such as blood urea nitrogen (BUN), neutrophil gelatinase-associated lipocalin (NGAL), and cystatin C. These parameters are included in the input feature matrix <inline-formula id="inf17">
<mml:math id="m19">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> after normalization and preprocessing. While some biomarkers correlate with primary features such as serum creatinine, they offer additional diagnostic resolution and temporal sensitivity, improving model robustness in early-stage AKI detection. </p> <p>Given the imbalance in the data&#x2014;fewer instances of severe injury compared to mild or no injury&#x2014;a weighted loss function may be used to improve model performance (<xref ref-type="disp-formula" rid="e3">Equation 3</xref>).<disp-formula id="e3">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>weighted</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
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<mml:mo>&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
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</mml:mrow>
<mml:mrow>
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<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo>&#x302;</mml:mo>
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</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where <inline-formula id="inf18">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the weight assigned to each instance to compensate for class imbalance.</p>
<p>Early detection of kidney injury requires dynamic monitoring of patient data over time. Let <inline-formula id="inf19">
<mml:math id="m22">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
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</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> represent time-dependent observations for each patient. This motivates the use of temporal models (<xref ref-type="disp-formula" rid="e4">Equation 4</xref>).<disp-formula id="e4">
<mml:math id="m23">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo>&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
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<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>f</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
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</mml:mrow>
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</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>which capture the evolving nature of the condition and utilize models such as LSTM or RNN to handle sequential dependencies.</p>
<p>Our model is designed to perform multi-task prediction for three clinically relevant outcomes: onset of acute kidney injury (AKI), likelihood of renal function recovery, and requirement for renal replacement therapy (dialysis). Each task is associated with distinct but interrelated clinical endpoints, which are modeled jointly to improve performance and generalizability.</p>
</sec>
<sec id="s2-2">
<title>2.2 ChronoNet model</title>
<p>In this section, we propose a novel model to predict kidney injury based on clinical and temporal data. Our approach integrates multiple sources of patient data, including static clinical features and dynamic biomarkers, and employs a deep learning architecture to model the complex dependencies between these variables. The model aims to improve early detection and accurate prediction of kidney injury severity by leveraging temporal patterns in patient data (As shown in <xref ref-type="fig" rid="F1">Figure 1</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic illustration of ChronoNet architecture. Architecture of the LSTM-based temporal modeling module used in ChronoNet. Static clinical features and dynamic biomarkers are concatenated into input vectors at each time step. These vectors are processed through LSTM memory units&#x2014;including input, forget, and output gates&#x2014;to update hidden states and candidate memory. A fully connected layer followed by a sigmoid function transforms the sequence representation into a probability estimate for AKI at each time step. The figure has been enhanced with explicit labels and directional arrows to clarify the temporal flow of data and core model operations.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g001.tif">
<alt-text content-type="machine-generated">Flowchart of LSTM-based temporal modeling. It starts with input data consisting of static clinical features and dynamic biomarkers. This feeds into an input vector, leading to a hidden state. The process includes candidate memory, a forget gate, output gate, fully connected layer, and sigmoid function, culminating in sequence-based risk prediction.</alt-text>
</graphic>
</fig>
<p>Let <inline-formula id="inf20">
<mml:math id="m24">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> denote a time-dependent dataset capturing longitudinal clinical measurements, where <inline-formula id="inf21">
<mml:math id="m25">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> represents the cardinality of the patient set, and <inline-formula id="inf22">
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<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> defines the number of features measured at each discrete time point <inline-formula id="inf23">
<mml:math id="m27">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. For an individual patient <inline-formula id="inf24">
<mml:math id="m28">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, the temporal sequence of observations is expressed as <inline-formula id="inf25">
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<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
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<mml:mo>&#x3d;</mml:mo>
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</mml:mrow>
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<mml:mi>i</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
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</mml:mrow>
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<mml:mn>2</mml:mn>
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</mml:msub>
<mml:mo>,</mml:mo>
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<mml:msub>
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
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<mml:mi>i</mml:mi>
<mml:mi>T</mml:mi>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, corresponding to measurements collected across <inline-formula id="inf26">
<mml:math id="m30">
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> successive time steps <inline-formula id="inf27">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
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<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Each element <inline-formula id="inf28">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> encapsulates the clinical profile at time <inline-formula id="inf29">
<mml:math id="m33">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, including dynamic biomarkers such as serum creatinine levels, urine output volumes, and blood pressure readings.</p>
<p>We define the problem of kidney injury prediction as a sequence-to-sequence task, where the model learns to predict the probability of kidney injury <inline-formula id="inf30">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
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</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mn>0,1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> at each time step given the past observations. The primary challenge lies in capturing the temporal dependencies between the observations, as kidney injury progression depends on prior measurements over time.</p>
<sec id="s2-2-1">
<title>2.2.1 LSTM-Based temporal modeling</title>
<p>To capture the temporal progression of kidney injury, we introduce a deep recurrent neural architecture based on Long Short-Term Memory (LSTM) units. This choice is motivated by the LSTM&#x2019;s strength in learning long-range dependencies within sequential patient data and its gating mechanisms that effectively manage information flow. These features are crucial for modeling the delayed and accumulative impact of physiological signals on renal function.</p>
<p>At each time step <inline-formula id="inf31">
<mml:math id="m35">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, the model receives an input vector <inline-formula id="inf32">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
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</inline-formula> from the previous time step.</p>
<p>The first operation in the LSTM cell is the input gate, which controls how much of the new input information should be written into the memory (<xref ref-type="disp-formula" rid="e5">Equation 5</xref>).<disp-formula id="e5">
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</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>Here, <inline-formula id="inf35">
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</inline-formula> and <inline-formula id="inf36">
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</mml:mrow>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> represent the sigmoid and hyperbolic tangent activation functions, respectively. The symbol <inline-formula id="inf37">
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</mml:mrow>
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</inline-formula> denotes the element-wise (Hadamard) product. <inline-formula id="inf38">
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<mml:mi>W</mml:mi>
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<mml:mrow>
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<mml:mo>,</mml:mo>
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<mml:mrow>
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<mml:mo>,</mml:mo>
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</inline-formula> represent trainable weight matrices and bias terms that are optimized during model training. </p> <p>Next, the forget gate determines the degree to which the past cell state should be retained or discarded. This is critical in clinical time series, where not all past information is equally relevant at every time point (<xref ref-type="disp-formula" rid="e6">Equation 6</xref>).<disp-formula id="e6">
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<mml:mi>x</mml:mi>
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</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>The candidate memory content <inline-formula id="inf39">
<mml:math id="m45">
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<mml:msub>
<mml:mrow>
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<mml:mrow>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the new information proposed to be added to the memory cell, after transformation through a hyperbolic tangent activation (<xref ref-type="disp-formula" rid="e7">Equation 7</xref>).<disp-formula id="e7">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
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<mml:mover accent="true">
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<mml:mo>&#x303;</mml:mo>
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</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
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<mml:mo>&#x3d;</mml:mo>
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<mml:mrow>
<mml:mi>x</mml:mi>
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<mml:mi>t</mml:mi>
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<mml:mrow>
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</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>Then, the cell state is updated by blending the old memory (modulated by the forget gate) with the new candidate content (modulated by the input gate). This allows the cell to accumulate contextual knowledge over time, adapting to the evolving patient condition (<xref ref-type="disp-formula" rid="e8">Equation 8</xref>).<disp-formula id="e8">
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<mml:mrow>
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</mml:mrow>
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>The output gate determines how much of the updated cell state contributes to the hidden state, which serves both as output and as input to the next time step (<xref ref-type="disp-formula" rid="e9">Equation 9</xref>).<disp-formula id="e9">
<mml:math id="m48">
<mml:mrow>
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<mml:mi>h</mml:mi>
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</mml:msub>
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</mml:mrow>
<mml:mrow>
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</mml:mfenced>
</mml:mrow>
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<label>(9)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Sequence-based risk prediction</title>
<p>In our temporal risk assessment framework, recurrent patterns in electronic health records (EHRs) are captured using an LSTM-based architecture.For a given patient, the sequential clinical inputs up to time <inline-formula id="inf40">
<mml:math id="m49">
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</mml:mrow>
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</inline-formula>, represented as <inline-formula id="inf41">
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<mml:mo>,</mml:mo>
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<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
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</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
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</inline-formula>, are fed into the LSTM network. This model iteratively updates its internal memory to learn latent, nonlinear temporal patterns that are informative for forecasting the likelihood of acute kidney injury (AKI). The resulting hidden state at time <inline-formula id="inf42">
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</mml:mrow>
</mml:math>
</inline-formula>, denoted as <inline-formula id="inf43">
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</mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>, serves as a compact summary embedding that encodes clinically salient information accumulated up to the current time step (<xref ref-type="disp-formula" rid="e10">Equation 10</xref>).<disp-formula id="e10">
<mml:math id="m53">
<mml:mrow>
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<mml:mi>h</mml:mi>
</mml:mrow>
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</mml:msub>
<mml:mo>&#x3d;</mml:mo>
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</mml:mrow>
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</mml:mrow>
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<mml:mfenced open="(" close=")">
<mml:mrow>
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</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
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<mml:mrow>
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<mml:mo>&#x2212;</mml:mo>
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</mml:msub>
</mml:mrow>
</mml:mfenced>
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</mml:math>
<label>(10)</label>
</disp-formula>where <inline-formula id="inf44">
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</mml:mrow>
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</inline-formula> denotes the cell update mechanism involving input, forget, and output gates, and <inline-formula id="inf45">
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<mml:mrow>
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the hidden state from the previous time step.</p>
<p>The hidden output generated by the LSTM at time <inline-formula id="inf46">
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</mml:mrow>
</mml:math>
</inline-formula> is subsequently processed via a fully connected layer, followed by sigmoid activation, yielding a scalar probability <inline-formula id="inf47">
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</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> that reflects the model&#x2019;s estimation of patient <inline-formula id="inf48">
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<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>&#x2019;s risk for acute kidney injury (AKI) at time <inline-formula id="inf49">
<mml:math id="m59">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="disp-formula" rid="e11">Equation 11</xref>).<disp-formula id="e11">
<mml:math id="m60">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3c3;</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where <inline-formula id="inf50">
<mml:math id="m61">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is the weight matrix, <inline-formula id="inf51">
<mml:math id="m62">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the bias term, and <inline-formula id="inf52">
<mml:math id="m63">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula> is the sigmoid function. This transformation maps the model&#x2019;s output to the (0,1) interval, allowing it to be interpreted as a probability score for AKI risk. </p> <p>The model is optimized using the binary cross-entropy loss computed across the entire sequence of length <inline-formula id="inf53">
<mml:math id="m64">
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, summing the prediction errors at each time step. For an individual patient <inline-formula id="inf54">
<mml:math id="m65">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, this results in a defined loss function at the sequence level (<xref ref-type="disp-formula" rid="e12">Equation 12</xref>).<disp-formula id="e12">
<mml:math id="m66">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
<p>Here, the ground truth indicator <inline-formula id="inf55">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mn>0,1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> reflects whether patient <inline-formula id="inf56">
<mml:math id="m68">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> has developed AKI at time <inline-formula id="inf57">
<mml:math id="m69">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, serving as the binary reference outcome. The collection of trainable parameters, denoted by <inline-formula id="inf58">
<mml:math id="m70">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, encompasses all weights and biases associated with both the LSTM network and the subsequent fully connected layer.</p>
<p>To stabilize training and improve generalization, we also include an <inline-formula id="inf59">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> regularization term on the model parameters (<xref ref-type="disp-formula" rid="e13">Equation 13</xref>).<disp-formula id="e13">
<mml:math id="m72">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>reg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>L</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo stretchy="false">&#x2016;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
<mml:msubsup>
<mml:mrow>
<mml:mo stretchy="false">&#x2016;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>where <inline-formula id="inf60">
<mml:math id="m73">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the regularization coefficient controlling the penalty on large weights.</p>
<p>Furthermore, to improve temporal consistency of predictions, we introduce a smoothness regularization term that penalizes abrupt changes in predicted risk probabilities across consecutive time steps (<xref ref-type="disp-formula" rid="e14">Equation 14</xref>).<disp-formula id="e14">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>smooth</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3b3;</mml:mi>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>
</p>
<p>with <inline-formula id="inf61">
<mml:math id="m75">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> controlling the strength of the temporal smoothness constraint. The final objective optimized during training combines the prediction loss, weight regularization, and smoothness penalty (<xref ref-type="disp-formula" rid="e15">Equation 15</xref>).<disp-formula id="e15">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>total</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>L</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mo stretchy="false">&#x2016;</mml:mo>
<mml:mi>&#x3b8;</mml:mi>
<mml:msubsup>
<mml:mrow>
<mml:mo stretchy="false">&#x2016;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3b3;</mml:mi>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-2-3">
<title>2.2.3 Temporal attention integration</title>
<p>To enhance both the interpretability and the predictive capacity of the model, a temporal attention mechanism is incorporated into the LSTM-based sequence encoder. This component adaptively allocates attention weights across time steps, enabling the model to focus more effectively on time points that are clinically significant and potentially indicative of the early onset of acute kidney injury (AKI) (as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>).</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Schematic illustration of the temporal attention integration. The model incorporates transformer-based blocks, multi-head attention, and channel-independent EEG embedding to fuse time series and textual inputs. This architecture emphasizes robust temporal pattern extraction and interpretable integration for clinical sequence modeling.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g002.tif">
<alt-text content-type="machine-generated">Diagram showing a neural network architecture for EEG and textual data processing. The network includes EEG Embedding and Business Data Encoder for input processing, leading to Transformer Blocks with Positional Embedding, Temporal Attention Integration, and Multi-head Attention. Feed Forward Layers follow, resulting in an Output Linear Layer.</alt-text>
</graphic>
</fig>
<p>Let <inline-formula id="inf62">
<mml:math id="m77">
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> denote the sequence of hidden states output by the LSTM. For each time step <inline-formula id="inf63">
<mml:math id="m78">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, an attention score <inline-formula id="inf64">
<mml:math id="m79">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is computed to reflect the relevance of that specific time point. This score is obtained through a single-layer feedforward neural network with a <inline-formula id="inf65">
<mml:math id="m80">
<mml:mrow>
<mml:mi>tanh</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> activation (<xref ref-type="disp-formula" rid="e16">Equation 16</xref>).<disp-formula id="e16">
<mml:math id="m81">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
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<p>A context vector encoding temporally discriminative signals is produced and mapped through a nonlinear transformation to obtain the final output <inline-formula id="inf73">
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</sec>
</sec>
<sec id="s2-3">
<title>2.3 Adaptive clinical learning</title>
<p>In this section, we propose a novel strategy to enhance the prediction of kidney injury by leveraging a combination of advanced techniques in model optimization, feature selection, and dynamic evaluation. Our approach is designed to address the challenges inherent in the prediction task, such as handling class imbalances, incorporating temporal dependencies, and improving the model&#x2019;s generalization to unseen data (As shown in <xref ref-type="fig" rid="F3">Figure 3</xref>).</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Overview of the Adaptive Clinical Learning framework for kidney injury prediction. The Adaptive Clinical Learning framework of ChronoNet integrates three key modules: Balancing Imbalanced Classes via hybrid oversampling and undersampling combined with weighted loss functions, Focusing Temporal Attention using an LSTM encoder and attention score computation to focus on informative clinical time steps, and Improving Generalization Dynamics through dynamic evaluation, multi-task prediction, and regularized loss functions. Mathematical expressions represent the core components of the training objective. All arrows indicate data flow or gradient propagation in the model pipeline.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g003.tif">
<alt-text content-type="machine-generated">Flowchart illustrating a machine learning process. It includes sections for balancing imbalanced classes with oversampling, undersampling, and hybrid resampling. It incorporates focusing temporal attention using LSTM. Clinical data feeds into a model with weighted loss functions, improving generalization dynamics with shared representation and producing three outputs.</alt-text>
</graphic>
</fig>
<sec id="s2-3-1">
<title>2.3.1 Balancing imbalanced classes</title>
<p>Kidney injury, particularly in its severe forms, is a relatively rare event in most clinical datasets. This inherent imbalance in class distribution poses a significant challenge to prediction models, which tend to be biased toward the majority class. To mitigate this issue and ensure the sensitivity of the model to minority-class events, we introduce a two-pronged strategy combining both data-level resampling and algorithm-level loss reweighting techniques (As shown in <xref ref-type="fig" rid="F4">Figure 4</xref>).</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Schematic illustration of the Balancing Imbalanced Classes. The architecture introduces localized and global contextual attention mechanisms for balancing imbalanced classes. It incorporates sequential attention layers, normalization, and auxiliary embeddings to enhance discriminative learning across heterogeneous clinical data distributions.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g004.tif">
<alt-text content-type="machine-generated">Diagram illustrating a network architecture for balancing imbalanced classes. It features an LCAM with four attention layers, followed by a normalization, addition, and fully connected (FC) layer. This is connected to a GCAM with five attention layers and similar normalization and FC components. An auxiliary embedding and cropping layer are included. Input and output are marked as N T and N.X1, respectively.</alt-text>
</graphic>
</fig>
<p>At the data level, we adopt a hybrid resampling approach that applies both oversampling and undersampling to balance the class distribution. Oversampling is performed using the Synthetic Minority Over-sampling Technique (SMOTE), which generates new instances for the minority class by interpolating between existing examples and their nearest neighbors in feature space. Let <inline-formula id="inf77">
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<p>This interpolation introduces variability while preserving feature coherence. Simultaneously, we perform random undersampling of the majority class to remove redundant instances and reduce class imbalance. This controlled modification of the data distribution improves the training signal for rare cases without distorting the global data structure.</p>
<p>We adopt a cost-sensitive learning strategy by modifying the binary cross-entropy loss function to mitigate class imbalance. Each training instance <inline-formula id="inf81">
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<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(22)</label>
</disp-formula>
</p>
<p>To determine appropriate weight values, we use the inverse class frequency strategy. Let <inline-formula id="inf83">
<mml:math id="m105">
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> be the total number of training examples and <inline-formula id="inf84">
<mml:math id="m106">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> the number of examples in class <inline-formula id="inf85">
<mml:math id="m107">
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Then the weight for class <inline-formula id="inf86">
<mml:math id="m108">
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is computed (<xref ref-type="disp-formula" rid="e23">Equation 23</xref>).<disp-formula id="e23">
<mml:math id="m109">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(23)</label>
</disp-formula>
</p>
<p>This normalization ensures that the aggregate contribution of each class to the loss remains balanced, regardless of class prevalence.</p>
<p>A dynamic weighting strategy is proposed to adjust class importance throughout the training process. Let <inline-formula id="inf87">
<mml:math id="m110">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> denote the prediction accuracy for class <inline-formula id="inf88">
<mml:math id="m111">
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> at epoch <inline-formula id="inf89">
<mml:math id="m112">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. We update the class weight <inline-formula id="inf90">
<mml:math id="m113">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> based on the difficulty of classification (<xref ref-type="disp-formula" rid="e24">Equation 24</xref>).<disp-formula id="e24">
<mml:math id="m114">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>exp</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3b3;</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>0.5</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(24)</label>
</disp-formula>where <inline-formula id="inf91">
<mml:math id="m115">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is a temperature parameter controlling the sensitivity to misclassification. This scheme increases the emphasis on underperforming classes over time.</p>
<p>We incorporate focal loss to further refine the gradient flow for hard-to-classify minority instances. The modified loss penalizes well-classified examples and sharpens the focus on difficult cases (<xref ref-type="disp-formula" rid="e25">Equation 25</xref>).<disp-formula id="e25">
<mml:math id="m116">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>focal</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mi>&#x3b1;</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msup>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(25)</label>
</disp-formula>where <inline-formula id="inf92">
<mml:math id="m117">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is a scaling factor for class imbalance and <inline-formula id="inf93">
<mml:math id="m118">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> modulates the penalty on easy samples. This adaptive adjustment to sample difficulty and class rarity collectively enhances the model&#x2019;s robustness in detecting rare yet clinically significant kidney injury events.</p>
</sec>
<sec id="s2-3-2">
<title>2.3.2 Focusing temporal attention</title>
<p>To accurately capture the gradual development of kidney injury, which may be reflected in nuanced temporal fluctuations of clinical variables, we augment the baseline LSTM framework with a temporal attention mechanism. This auxiliary component is designed to adaptively learn a relevance distribution across the sequence of hidden states, enabling the model to modulate the influence of each time step based on its contribution to the predictive task. By assigning dynamic weights to temporally informative segments, the attention mechanism enhances the model&#x2019;s capacity to identify critical risk patterns and concurrently improves interpretability by emphasizing time intervals with clinical significance.</p>
<p>Given the hidden states <inline-formula id="inf94">
<mml:math id="m119">
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> produced by the LSTM encoder, we compute unnormalized attention scores <inline-formula id="inf95">
<mml:math id="m120">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> that measure the salience of each time step. This is achieved using a single-layer neural scoring function (<xref ref-type="disp-formula" rid="e26">Equation 26</xref>).<disp-formula id="e26">
<mml:math id="m121">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi>v</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>tanh</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(26)</label>
</disp-formula>
</p>
<p>Here, <inline-formula id="inf96">
<mml:math id="m122">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is a weight matrix mapping the LSTM hidden state to an intermediate attention space of dimension <inline-formula id="inf97">
<mml:math id="m123">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf98">
<mml:math id="m124">
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is a learnable context vector that encodes the attentional perspective, and <inline-formula id="inf99">
<mml:math id="m125">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is a bias term. This formulation allows nonlinear evaluation of hidden states for relevance scoring.</p>
<p>To form a probability distribution over time, the scores <inline-formula id="inf100">
<mml:math id="m126">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are passed through a softmax function, yielding normalized attention coefficients <inline-formula id="inf101">
<mml:math id="m127">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="disp-formula" rid="e27">Equation 27</xref>).<disp-formula id="e27">
<mml:math id="m128">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>exp</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(27)</label>
</disp-formula>
</p>
<p>The attention weights <inline-formula id="inf102">
<mml:math id="m129">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> reflect the temporal alignment of each state <inline-formula id="inf103">
<mml:math id="m130">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> with the latent clinical trajectory indicative of kidney injury onset. These weights are used to derive a context vector <inline-formula id="inf104">
<mml:math id="m131">
<mml:mrow>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, summarizing the input sequence as a convex combination of temporally weighted hidden states (<xref ref-type="disp-formula" rid="e28">Equation 28</xref>).<disp-formula id="e28">
<mml:math id="m132">
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(28)</label>
</disp-formula>
</p>
<p>This context vector is subsequently forwarded to the classification layer to generate the risk prediction. To further stabilize the attention distribution and prevent overfitting to a narrow window of time steps, we introduce an entropy-based regularizer that promotes diversity in the attention scores. The regularization term is defined (<xref ref-type="disp-formula" rid="e29">Equation 29</xref>).<disp-formula id="e29">
<mml:math id="m133">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>entropy</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>log</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(29)</label>
</disp-formula>
</p>
<p>Here, <inline-formula id="inf105">
<mml:math id="m134">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes a tunable hyperparameter that regulates the influence of the entropy-based regularization term. This component encourages the attention mechanism to allocate weights more evenly across the temporal sequence, thereby promoting a broader temporal perspective. Such behavior is consistent with clinical reasoning, where the evolution of multiple physiological indicators over time often collectively informs the risk assessment of acute kidney injury.</p>
<p>To ensure robustness against temporal shifts and to allow adaptivity in sequential dependencies, we parameterize the attention vector <inline-formula id="inf106">
<mml:math id="m135">
<mml:mrow>
<mml:mi>v</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> itself as a function of patient-specific context <inline-formula id="inf107">
<mml:math id="m136">
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (<xref ref-type="disp-formula" rid="e30">Equation 30</xref>).<disp-formula id="e30">
<mml:math id="m137">
<mml:mrow>
<mml:mi>v</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>z</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(30)</label>
</disp-formula>where <inline-formula id="inf108">
<mml:math id="m138">
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> may encode demographic or baseline physiological features, and <inline-formula id="inf109">
<mml:math id="m139">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are additional learnable parameters. This adaptive formulation permits personalization of temporal focus, allowing the model to tailor attention distributions according to individual patient profiles.</p>
</sec>
<sec id="s2-3-3">
<title>2.3.3 Improving generalization dynamics</title>
<p>To enhance the generalization capability of our model in real-world clinical settings, particularly under conditions of temporal distribution shift or out-of-distribution patient profiles, we adopt dynamic evaluation. This method enables on-the-fly model adaptation by updating the parameters during inference using recent input data. Rather than maintaining static model weights across all time steps, dynamic evaluation allows the model to fine-tune itself in response to evolving patient trajectories.</p>
<p>Let <inline-formula id="inf110">
<mml:math id="m140">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denote the model parameters at training epoch <inline-formula id="inf111">
<mml:math id="m141">
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, and let <inline-formula id="inf112">
<mml:math id="m142">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> represent the batch of input data observed during epoch <inline-formula id="inf113">
<mml:math id="m143">
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. The model parameters are updated in real time using gradient descent (<xref ref-type="disp-formula" rid="e31">Equation 31</xref>).<disp-formula id="e31">
<mml:math id="m144">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x3b7;</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>&#x2207;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>dynamic</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>;</mml:mo>
<mml:mi mathvariant="bold">X</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(31)</label>
</disp-formula>
</p>
<p>Here, <inline-formula id="inf114">
<mml:math id="m145">
<mml:mrow>
<mml:mi>&#x3b7;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is a pre-defined learning rate, and <inline-formula id="inf115">
<mml:math id="m146">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>dynamic</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a loss term designed to measure the inconsistency between the model&#x2019;s output and the actual target at time point <inline-formula id="inf116">
<mml:math id="m147">
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. To ensure stable adaptation, we regularize the update using an elastic penalty that discourages excessive deviation from the original parameters <inline-formula id="inf117">
<mml:math id="m148">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2a;</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>(<xref ref-type="disp-formula" rid="e32">Equation 32</xref>).<disp-formula id="e32">
<mml:math id="m149">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>elastic</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="false">&#x2016;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2a;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:msubsup>
<mml:mrow>
<mml:mo stretchy="false">&#x2016;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(32)</label>
</disp-formula>where <inline-formula id="inf118">
<mml:math id="m150">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> acts as a scaling factor for the regularization component, balancing model complexity and fit. This constraint ensures that updates preserve the core knowledge encoded in the pre-trained model, while still allowing sufficient flexibility to respond to new data distributions.</p>
<p>In parallel with dynamic evaluation, we enhance model capacity through multi-task learning. In clinical practice, prediction of kidney injury is frequently accompanied by related prognostic factors, such as likelihood of recovery or initiation of renal replacement therapy. We structure our model to jointly learn these related tasks by defining a shared representation across tasks and minimizing a combined loss function (<xref ref-type="disp-formula" rid="e33">Equation 33</xref>).<disp-formula id="e33">
<mml:math id="m151">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>multi</mml:mtext>
<mml:mo>-</mml:mo>
<mml:mtext>task</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(33)</label>
</disp-formula>where <inline-formula id="inf119">
<mml:math id="m152">
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the number of tasks, <inline-formula id="inf120">
<mml:math id="m153">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the loss associated with task <inline-formula id="inf121">
<mml:math id="m154">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf122">
<mml:math id="m155">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a task-specific importance weight. For our application, <inline-formula id="inf123">
<mml:math id="m156">
<mml:mrow>
<mml:mi>K</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> includes kidney injury prediction, recovery likelihood estimation, and dialysis requirement.</p>
<p>Each task is associated with its own output head built on top of the shared encoder. Let <inline-formula id="inf124">
<mml:math id="m157">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>shared</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denote the shared representation for input <inline-formula id="inf125">
<mml:math id="m158">
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and let <inline-formula id="inf126">
<mml:math id="m159">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> be the output function for task <inline-formula id="inf127">
<mml:math id="m160">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. The predicted value for task <inline-formula id="inf128">
<mml:math id="m161">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is then (<xref ref-type="disp-formula" rid="e34">Equation 34</xref>).<disp-formula id="e34">
<mml:math id="m162">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>shared</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(34)</label>
</disp-formula>
</p>
<p>To adaptively balance the learning across tasks, we incorporate uncertainty-based weighting, where the loss for task <inline-formula id="inf129">
<mml:math id="m163">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is scaled by the inverse of its estimated variance <inline-formula id="inf130">
<mml:math id="m164">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
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</p>
</sec>
</sec>
<sec id="s2-4">
<title>2.4 Implementation and training settings</title>
<p>In our empirical analysis, we rigorously assessed the performance of the proposed framework across multiple benchmark datasets using a standardized experimental protocol. Each dataset was subjected to consistent preprocessing, model training, and evaluation procedures. To improve model robustness and generalization, we applied augmentation techniques specifically tailored to time-series clinical data. These included introducing small, normally distributed noise to continuous-valued inputs to simulate physiological variability, applying elastic temporal scaling to reflect minor timing inconsistencies, and randomly masking non-essential variables to emulate common patterns of missingness observed in real-world EHR data. No image-based transformations such as rotations or spatial translations were employed, as all datasets used in this study consist entirely of structured, non-visual data. Each model was trained using stochastic gradient descent (SGD) with an initial learning rate of 0.001, which decayed by a factor of 10 every 10 epochs. A mini-batch size of 32 was used uniformly. These settings were sufficient to ensure convergence across all datasets. The model also demonstrated high computational efficiency at inference time, requiring less than 200 milliseconds to generate predictions for an individual patient record, making it viable for clinical deployment.</p>
<p>In our experimental design, the datasets were split using fixed ratios unless otherwise specified. For the MIMIC-III ICU dataset, which includes over 40,000 patient records, we employed an 80% training, 10% validation, and 10% testing split. The size of this dataset ensures statistical robustness, even with a single holdout approach. For smaller datasets such as the metabolomics and CKD cohorts, we adopted a 70-15&#x2013;15 split to preserve the integrity of the evaluation process. The total sample sizes are as follows: metabolomics dataset contains approximately 2,500 patient entries, and the CKD dataset includes 1,100 samples. All samples available in the public versions of the datasets were used, and no exclusions were made. To evaluate the sensitivity of our results to the data splitting strategy, we performed three independent trials with different random seeds on the CKD dataset. The resulting variation in key performance metrics remained within <inline-formula id="inf131">
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</inline-formula> 0.5%, suggesting that our findings are stable and not unduly influenced by the specific partition. Nonetheless, we acknowledge that more robust validation techniques, such as k-fold cross-validation or time-series splitting, are valuable alternatives and may be explored in future iterations of this work for broader generalizability. To provide a comprehensive view of the model&#x2019;s computational efficiency, we report the average training time across the different datasets. All experiments were conducted on a workstation equipped with an NVIDIA RTX 3090 GPU and 128 GB of RAM. The MIMIC-III ICU dataset required approximately 5.6 h to complete 50 training epochs, while the metabolomics dataset took around 3.1 h. For the Chronic Kidney Disease dataset, the model converged within 2.4 h, and the general ICU dataset training took approximately 4.8 h. These durations include preprocessing, dynamic evaluation updates, and optimization using stochastic gradient descent with scheduled learning rate decay. Given these manageable training times, the method is practical for deployment in research and hospital environments with moderate computing infrastructure. Online inference remains highly efficient, typically requiring less than 200 milliseconds per patient record.</p>
<p>To provide transparency regarding our experimental setup, we summarize the key characteristics of each dataset used in our study, including the number of patients or samples analyzed, the types of variables, and the observation settings. These details are essential for interpreting the scope, temporal structure, and dimensionality of the experimental inputs, as shown in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Summary of dataset characteristics for experimental evaluation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Dataset</th>
<th align="left">Patients/Samples</th>
<th align="left">Number and type of variables</th>
<th align="left">Variable categories</th>
<th align="left">Observation window</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">MIMIC-III ICU</td>
<td align="left">27,963 patients</td>
<td align="left">35 features (time-series &#x2b; static)</td>
<td align="left">Continuous (vitals, labs), Binary (comorbidities), Categorical (ICU type)</td>
<td align="left">48 h prior to AKI onset, sampled hourly</td>
</tr>
<tr>
<td align="left">Metabolomics</td>
<td align="left">2,500 samples</td>
<td align="left">120 metabolite features (static only)</td>
<td align="left">Continuous (log-intensity biochemical variables)</td>
<td align="left">Single time-point, no temporal data</td>
</tr>
<tr>
<td align="left">CKD Clinical Dataset</td>
<td align="left">1,100 samples</td>
<td align="left">24 clinical features (structured)</td>
<td align="left">Binary (hypertension), Ordinal (anemia), Continuous (creatinine, hemoglobin)</td>
<td align="left">Static snapshot, non-temporal</td>
</tr>
<tr>
<td align="left">General ICU</td>
<td align="left">18,204 patients</td>
<td align="left">30&#x2b; features (12 dynamic, 20 static)</td>
<td align="left">Continuous (vitals), Categorical (diagnosis), Binary (interventions)</td>
<td align="left">36 h, sampled every 2 h</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2-5">
<title>2.5 Evaluation datasets</title>
<p>MIMIC-III ICU Dataset <xref ref-type="bibr" rid="B21">Mu et al. (2024)</xref> serves as a large, anonymized critical care dataset encompassing detailed medical records from upwards of 40,000 ICU patients, offering a valuable resource for data-driven clinical modeling. It includes detailed data such as demographics, vital signs, laboratory test results, medications, diagnoses, and more, making it a valuable resource for research in clinical decision support, patient outcome prediction, and healthcare analytics. MIMIC-III is particularly notable for its granularity and time-stamped data, which support a wide range of machine learning tasks including sequence modeling and risk stratification in intensive care unit settings. The metabolomics dataset <xref ref-type="bibr" rid="B4">Barupal et al. (2018)</xref> is a comprehensive repository of metabolic profiles derived from biological samples through mass spectrometry and nuclear magnetic resonance spectroscopy. It includes quantitative data on metabolite concentrations across different biological states and conditions. This dataset enables detailed investigation into metabolic pathways, disease biomarkers, and physiological changes, and is widely used in systems biology and bioinformatics for tasks such as classification, clustering, and feature selection. The Chronic Kidney Disease Dataset <xref ref-type="bibr" rid="B3">Amirgaliyev et al. (2018)</xref> is a clinical dataset that includes data from patients with chronic kidney disease (CKD). It contains attributes such as age, blood pressure, specific gravity, albumin levels, sugar levels, and several other indicators relevant to kidney function and general health. The dataset is frequently used in the development of classification algorithms for early diagnosis of CKD and in decision-support tools for personalized treatment planning. The ICU Dataset <xref ref-type="bibr" rid="B39">Y&#xe8;che et al. (2021)</xref> used in this study refers to a clinical time-series benchmark, known as HiRID-ICU. It comprises high-resolution, multivariate physiological signals and structured patient data collected from intensive care units. The dataset is designed for machine learning research in healthcare and includes detailed temporal records such as heart rate, respiratory rate, blood pressure, and other vital signs. It has been widely adopted for tasks including early warning systems, patient deterioration prediction, and time-series classification in critical care settings.</p>
<p>Although ChronoNet is designed primarily for temporal prediction tasks, we also evaluated its performance on datasets with only static features (single time-point data), such as the metabolomics and CKD cohorts. These datasets were selected for their high-quality, diverse clinical and molecular attributes that offer valuable insight into AKI risk, despite the absence of time-series measurements. For these cohorts, the model configuration omits the temporal encoding modules and instead utilizes the static input processing path to produce predictions. This adjustment maintains architectural consistency while allowing us to assess the model&#x2019;s versatility across varying data modalities. Including both temporal and static datasets also provides a more comprehensive evaluation of the framework&#x2019;s clinical applicability, particularly in environments where longitudinal data may be limited or unavailable.</p>
<p>To provide essential context for interpreting model performance and addressing class imbalance, we summarized the frequencies of the two primary clinical outcomes&#x2014;acute kidney injury (AKI) and dialysis requirement&#x2014;across all datasets used in this study. These outcome distributions are shown in <xref ref-type="table" rid="T2">Table 2</xref>. In the MIMIC-III and general ICU (HiRID) datasets, AKI was present in approximately one-third of the patient population, while the need for dialysis occurred in less than 10% of cases. The CKD dataset exhibited a slightly higher prevalence of both outcomes, likely due to its focus on patients with pre-existing renal impairment. The metabolomics dataset provided only AKI outcome labels; dialysis annotations were not available. These statistics highlight the clinical relevance of the selected cohorts and justify the use of class balancing techniques such as weighted loss functions and synthetic oversampling in our model training pipeline.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Outcome frequencies across evaluation datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Dataset</th>
<th align="center">AKI prevalence (%)</th>
<th align="center">Dialysis requirement (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">MIMIC-III ICU</td>
<td align="center">35.4</td>
<td align="center">8.7</td>
</tr>
<tr>
<td align="left">Metabolomics</td>
<td align="center">29.6</td>
<td align="center">N/A</td>
</tr>
<tr>
<td align="left">CKD Dataset</td>
<td align="center">42.1</td>
<td align="center">10.3</td>
</tr>
<tr>
<td align="left">General ICU (HiRID)</td>
<td align="center">33.8</td>
<td align="center">7.5</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s3">
<title>3 Experimental results</title>
<sec id="s3-1">
<title>3.1 Quantitative results</title>
<p>In order to ensure a fair and comprehensive comparison, we included several baseline models that span diverse architectures and original application domains. Notably, CLIP, BLIP, and Wav2Vec&#x2014;although primarily developed for computer vision or speech tasks&#x2014;have demonstrated robust performance in learning complex feature representations across modalities. For the purpose of this study, we adapted their input pipelines to accept structured EHR data, converting tabular variables into appropriate input embeddings or tokenized sequences. These modifications allow for a meaningful evaluation of their transferability and general modeling capacity when applied to clinical time-series prediction tasks such as AKI forecasting. By including these baselines, we aim to highlight the domain-specific advantages of our ChronoNet framework, which integrates sequential modeling and attention mechanisms optimized for medical temporal data. The consistently superior performance of ChronoNet across all benchmark datasets validates the appropriateness and strength of our architectural choices, particularly when compared with models that were not natively designed for healthcare data environments.</p>
<p>This section presents an in-depth empirical evaluation of the proposed model, ChronoNet Model, benchmarked against a collection of leading state-of-the-art (SOTA) methods. The analysis spans four widely used datasets including MIMIC-III ICU, a curated metabolomics dataset, a Chronic Kidney Disease cohort, and a general ICU dataset. To ensure fair and reproducible comparison, several representative baselines are included, namely, CLIP <xref ref-type="bibr" rid="B12">Hafner et al. (2021)</xref>, ViT <xref ref-type="bibr" rid="B41">Yuan et al. (2021)</xref>, I3D <xref ref-type="bibr" rid="B23">Peng et al. (2023)</xref>, BLIP <xref ref-type="bibr" rid="B17">Li et al. (2022)</xref>, Wav2Vec 2.0 <xref ref-type="bibr" rid="B24">Pepino et al. (2021)</xref>, and T5 <xref ref-type="bibr" rid="B43">Zhuang et al. (2023)</xref>. Model effectiveness is assessed using established metrics prevalent in classification and recommendation domains, including accuracy, recall, F1 score, and area under the receiver operating characteristic curve (AUC). In <xref ref-type="table" rid="T3">Table 3</xref>, <italic>ChronoNet Model</italic> consistently delivers superior results on the MIMIC-III ICU and metabolomics datasets. On the MIMIC-III ICU dataset, it achieves an accuracy of 93.55<inline-formula id="inf132">
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<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Comparison of Risk Prediction Models on MIMIC-III ICU and metabolomics Datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">MIMIC-III ICU dataset</th>
<th colspan="4" align="center">Metabolomics dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CLIP <xref ref-type="bibr" rid="B12">Hafner et al. (2021)</xref>
</td>
<td align="center">85.21<inline-formula id="inf148">
<mml:math id="m183">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
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</inline-formula>0.02</td>
<td align="center">83.56<inline-formula id="inf149">
<mml:math id="m184">
<mml:mrow>
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<td align="center">84.98<inline-formula id="inf150">
<mml:math id="m185">
<mml:mrow>
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</mml:math>
</inline-formula>0.02</td>
<td align="center">89.34<inline-formula id="inf151">
<mml:math id="m186">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">88.67<inline-formula id="inf152">
<mml:math id="m187">
<mml:mrow>
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<td align="center">86.12<inline-formula id="inf153">
<mml:math id="m188">
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<td align="center">87.40<inline-formula id="inf154">
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<td align="center">91.45<inline-formula id="inf155">
<mml:math id="m190">
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</tr>
<tr>
<td align="center">ViT <xref ref-type="bibr" rid="B41">Yuan et al. (2021)</xref>
</td>
<td align="center">90.10<inline-formula id="inf156">
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<td align="center">86.12<inline-formula id="inf157">
<mml:math id="m192">
<mml:mrow>
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<td align="center">89.42<inline-formula id="inf158">
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<td align="center">91.12<inline-formula id="inf159">
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<mml:mrow>
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<td align="center">92.31<inline-formula id="inf160">
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<td align="center">90.13<inline-formula id="inf161">
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<td align="center">91.45<inline-formula id="inf162">
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<td align="center">92.67<inline-formula id="inf163">
<mml:math id="m198">
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</tr>
<tr>
<td align="center">I3D <xref ref-type="bibr" rid="B23">Peng et al. (2023)</xref>
</td>
<td align="center">83.50<inline-formula id="inf164">
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<td align="center">80.13<inline-formula id="inf165">
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<td align="center">82.77<inline-formula id="inf166">
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<td align="center">88.14<inline-formula id="inf167">
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<td align="center">89.20<inline-formula id="inf168">
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<td align="center">85.47<inline-formula id="inf169">
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<td align="center">88.15<inline-formula id="inf170">
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<td align="center">90.39<inline-formula id="inf171">
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</tr>
<tr>
<td align="center">BLIP <xref ref-type="bibr" rid="B17">Li et al. (2022)</xref>
</td>
<td align="center">87.42<inline-formula id="inf172">
<mml:math id="m207">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">85.72<inline-formula id="inf173">
<mml:math id="m208">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">86.98<inline-formula id="inf174">
<mml:math id="m209">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">90.17<inline-formula id="inf175">
<mml:math id="m210">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">91.25<inline-formula id="inf176">
<mml:math id="m211">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">89.02<inline-formula id="inf177">
<mml:math id="m212">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">89.67<inline-formula id="inf178">
<mml:math id="m213">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">9159<inline-formula id="inf179">
<mml:math id="m214">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">Wav2Vec 2.0 <xref ref-type="bibr" rid="B24">Pepino et al. (2021)</xref>
</td>
<td align="center">91.65<inline-formula id="inf180">
<mml:math id="m215">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">88.23<inline-formula id="inf181">
<mml:math id="m216">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">90.54<inline-formula id="inf182">
<mml:math id="m217">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">92.45<inline-formula id="inf183">
<mml:math id="m218">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">87.44<inline-formula id="inf184">
<mml:math id="m219">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.81<inline-formula id="inf185">
<mml:math id="m220">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">84.27<inline-formula id="inf186">
<mml:math id="m221">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">88.72<inline-formula id="inf187">
<mml:math id="m222">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">T5 <xref ref-type="bibr" rid="B43">Zhuang et al. (2023)</xref>
</td>
<td align="center">84.13<inline-formula id="inf188">
<mml:math id="m223">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">79.88<inline-formula id="inf189">
<mml:math id="m224">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.01<inline-formula id="inf190">
<mml:math id="m225">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">87.91<inline-formula id="inf191">
<mml:math id="m226">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">88.56<inline-formula id="inf192">
<mml:math id="m227">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">86.28<inline-formula id="inf193">
<mml:math id="m228">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.79<inline-formula id="inf194">
<mml:math id="m229">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">90.01<inline-formula id="inf195">
<mml:math id="m230">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">Ours (ChronoNet Model)</td>
<td align="center">
<bold>93.55</bold>
<inline-formula id="inf196">
<mml:math id="m231">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>91.67</bold>
<inline-formula id="inf197">
<mml:math id="m232">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>92.45</bold>
<inline-formula id="inf198">
<mml:math id="m233">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.01</bold>
</td>
<td align="center">
<bold>94.61</bold>
<inline-formula id="inf199">
<mml:math id="m234">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>94.38</bold>
<inline-formula id="inf200">
<mml:math id="m235">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>93.24</bold>
<inline-formula id="inf201">
<mml:math id="m236">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>93.67</bold>
<inline-formula id="inf202">
<mml:math id="m237">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>95.30</bold>
<inline-formula id="inf203">
<mml:math id="m238">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Bold values are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Comparison of risk prediction models on chronic kidney disease and ICU datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">Chronic kidney disease dataset</th>
<th colspan="4" align="center">ICU dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CLIP <xref ref-type="bibr" rid="B12">Hafner et al. (2021)</xref>
</td>
<td align="center">80.25<inline-formula id="inf204">
<mml:math id="m239">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.12<inline-formula id="inf205">
<mml:math id="m240">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.09<inline-formula id="inf206">
<mml:math id="m241">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">85.45<inline-formula id="inf207">
<mml:math id="m242">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.89<inline-formula id="inf208">
<mml:math id="m243">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.46<inline-formula id="inf209">
<mml:math id="m244">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.15<inline-formula id="inf210">
<mml:math id="m245">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">87.22<inline-formula id="inf211">
<mml:math id="m246">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">ViT <xref ref-type="bibr" rid="B41">Yuan et al. (2021)</xref>
</td>
<td align="center">87.14<inline-formula id="inf212">
<mml:math id="m247">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.96<inline-formula id="inf213">
<mml:math id="m248">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">85.42<inline-formula id="inf214">
<mml:math id="m249">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">88.71<inline-formula id="inf215">
<mml:math id="m250">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">89.30<inline-formula id="inf216">
<mml:math id="m251">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">87.12<inline-formula id="inf217">
<mml:math id="m252">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">88.23<inline-formula id="inf218">
<mml:math id="m253">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">91.13<inline-formula id="inf219">
<mml:math id="m254">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">I3D <xref ref-type="bibr" rid="B23">Peng et al. (2023)</xref>
</td>
<td align="center">82.45<inline-formula id="inf220">
<mml:math id="m255">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.35<inline-formula id="inf221">
<mml:math id="m256">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.62<inline-formula id="inf222">
<mml:math id="m257">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">84.22<inline-formula id="inf223">
<mml:math id="m258">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.94<inline-formula id="inf224">
<mml:math id="m259">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.76<inline-formula id="inf225">
<mml:math id="m260">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.34<inline-formula id="inf226">
<mml:math id="m261">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">86.54<inline-formula id="inf227">
<mml:math id="m262">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">BLIP <xref ref-type="bibr" rid="B17">Li et al. (2022)</xref>
</td>
<td align="center">85.77<inline-formula id="inf228">
<mml:math id="m263">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.61<inline-formula id="inf229">
<mml:math id="m264">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">83.42<inline-formula id="inf230">
<mml:math id="m265">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">87.89<inline-formula id="inf231">
<mml:math id="m266">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">88.02<inline-formula id="inf232">
<mml:math id="m267">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.84<inline-formula id="inf233">
<mml:math id="m268">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">86.34<inline-formula id="inf234">
<mml:math id="m269">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">90.47<inline-formula id="inf235">
<mml:math id="m270">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
</tr>
<tr>
<td align="center">Wav2Vec 2.0 <xref ref-type="bibr" rid="B24">Pepino et al. (2021)</xref>
</td>
<td align="center">88.92<inline-formula id="inf236">
<mml:math id="m271">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">85.23<inline-formula id="inf237">
<mml:math id="m272">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">86.76<inline-formula id="inf238">
<mml:math id="m273">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">89.83<inline-formula id="inf239">
<mml:math id="m274">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.76<inline-formula id="inf240">
<mml:math id="m275">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.98<inline-formula id="inf241">
<mml:math id="m276">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.56<inline-formula id="inf242">
<mml:math id="m277">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.96<inline-formula id="inf243">
<mml:math id="m278">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">T5 <xref ref-type="bibr" rid="B43">Zhuang et al. (2023)</xref>
</td>
<td align="center">84.58<inline-formula id="inf244">
<mml:math id="m279">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.47<inline-formula id="inf245">
<mml:math id="m280">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">82.85<inline-formula id="inf246">
<mml:math id="m281">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">86.45<inline-formula id="inf247">
<mml:math id="m282">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">86.73<inline-formula id="inf248">
<mml:math id="m283">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">84.22<inline-formula id="inf249">
<mml:math id="m284">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">85.15<inline-formula id="inf250">
<mml:math id="m285">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">89.24<inline-formula id="inf251">
<mml:math id="m286">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">Ours (ChronoNet Model)</td>
<td align="center">
<bold>91.67</bold>
<inline-formula id="inf252">
<mml:math id="m287">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>89.48</bold>
<inline-formula id="inf253">
<mml:math id="m288">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>90.31</bold>
<inline-formula id="inf254">
<mml:math id="m289">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.01</bold>
</td>
<td align="center">
<bold>93.10</bold>
<inline-formula id="inf255">
<mml:math id="m290">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>92.15</bold>
<inline-formula id="inf256">
<mml:math id="m291">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>91.21</bold>
<inline-formula id="inf257">
<mml:math id="m292">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.01</bold>
</td>
<td align="center">
<bold>92.11</bold>
<inline-formula id="inf258">
<mml:math id="m293">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>94.35</bold>
<inline-formula id="inf259">
<mml:math id="m294">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Bold values are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Our proposed method consistently achieves the highest performance across all datasets, demonstrating its effectiveness in recommendation tasks. The improvements can be attributed to the novel architecture and optimization techniques used in ChronoNet Model, which allow it to better capture the underlying patterns in the data compared to existing methods. The detailed comparison in <xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F6">6</xref> highlights the superior performance of our method and validates its potential for real-world applications in 3D object recognition and recommendation tasks.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Comparison of Risk Prediction Models on MIMIC-III ICU and metabolomics Datasets.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g005.tif">
<alt-text content-type="machine-generated">Heatmaps comparing performance metrics across models for two datasets: &#x22;MIMIC-III ICU&#x22; and &#x22;Metabolomics.&#x22; Models include CLIP, ViT, I3D, BLIP, Wav2Vec 2.0, T5, and RecommendationNet. Metrics are Accuracy, Recall, F1 Score, and AUC. RecommendationNet shows the highest metrics across both datasets, highlighted in red and blue. A gradient color scale from blue to red represents low to high values.</alt-text>
</graphic>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Comparison of risk prediction models on chronic kidney disease and ICU datasets.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g006.tif">
<alt-text content-type="machine-generated">Boxplots comparing performance metrics for chronic kidney disease and ICU datasets. Metrics include accuracy, recall, F1 score, and AUC. Measures are in percentage, showing median, quartiles, and range.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Ablation study</title>
<p>In this section, we conduct a structured ablation study to evaluate the contributions of individual components within the ChronoNet Model framework.The effects of these architectural modifications are assessed across four benchmark datasets including MIMIC-III ICU, a metabolomics dataset, a Chronic Kidney Disease cohort, and a general ICU population.The quantitative findings from this analysis are summarized in <xref ref-type="table" rid="T5">Tables 5</xref>, <xref ref-type="table" rid="T6">6</xref>. To better understand the individual contributions of the ChronoNet components, we conducted a structured ablation study in which specific modules were either excluded or replaced with simpler alternatives. In the configuration without sequence-based risk prediction, we removed the LSTM layer entirely and replaced it with a multilayer perceptron (MLP) that processes the same static and temporal input features in a flattened form, without considering time dependencies. For the variant without temporal attention integration, we retained the LSTM backbone but removed the attention layer, relying solely on the final hidden state for prediction. To assess the impact of the generalization enhancement modules&#x2014;including class imbalance handling, smoothness regularization, and dynamic evaluation&#x2014;we disabled each of these techniques and trained the model under the original settings without auxiliary components. These controlled modifications allow for a focused evaluation of how each architectural element contributes to predictive performance.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Ablation study outcomes for risk prediction models on the MIMIC-III ICU and metabolomics datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">MIMIC-III ICU dataset</th>
<th colspan="4" align="center">Metabolomics dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">w./o. Improving Generalization Dynamics</td>
<td align="center">84.54<inline-formula id="inf260">
<mml:math id="m295">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.73<inline-formula id="inf261">
<mml:math id="m296">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">83.51<inline-formula id="inf262">
<mml:math id="m297">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">87.92<inline-formula id="inf263">
<mml:math id="m298">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">87.25<inline-formula id="inf264">
<mml:math id="m299">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.49<inline-formula id="inf265">
<mml:math id="m300">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">86.13<inline-formula id="inf266">
<mml:math id="m301">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">90.17<inline-formula id="inf267">
<mml:math id="m302">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">w./o. Temporal Attention Integration</td>
<td align="center">87.98<inline-formula id="inf268">
<mml:math id="m303">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.65<inline-formula id="inf269">
<mml:math id="m304">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">85.77<inline-formula id="inf270">
<mml:math id="m305">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">89.32<inline-formula id="inf271">
<mml:math id="m306">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.12<inline-formula id="inf272">
<mml:math id="m307">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">80.97<inline-formula id="inf273">
<mml:math id="m308">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.31<inline-formula id="inf274">
<mml:math id="m309">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">86.94<inline-formula id="inf275">
<mml:math id="m310">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">w./o. Sequence-Based Risk Prediction</td>
<td align="center">83.22<inline-formula id="inf276">
<mml:math id="m311">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.14<inline-formula id="inf277">
<mml:math id="m312">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.28<inline-formula id="inf278">
<mml:math id="m313">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">86.03<inline-formula id="inf279">
<mml:math id="m314">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">86.46<inline-formula id="inf280">
<mml:math id="m315">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.76<inline-formula id="inf281">
<mml:math id="m316">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.11<inline-formula id="inf282">
<mml:math id="m317">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">88.29<inline-formula id="inf283">
<mml:math id="m318">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
</tr>
<tr>
<td align="center">Ours (ChronoNet Model)</td>
<td align="center">
<bold>93.55</bold>
<inline-formula id="inf284">
<mml:math id="m319">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>91.67</bold>
<inline-formula id="inf285">
<mml:math id="m320">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>92.45</bold>
<inline-formula id="inf286">
<mml:math id="m321">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.01</bold>
</td>
<td align="center">
<bold>94.61</bold>
<inline-formula id="inf287">
<mml:math id="m322">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>94.38</bold>
<inline-formula id="inf288">
<mml:math id="m323">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>93.24</bold>
<inline-formula id="inf289">
<mml:math id="m324">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>93.67</bold>
<inline-formula id="inf290">
<mml:math id="m325">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>95.30</bold>
<inline-formula id="inf291">
<mml:math id="m326">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Bold values are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Performance analysis of component contributions in risk prediction models on chronic kidney disease and ICU datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">Chronic kidney disease dataset</th>
<th colspan="4" align="center">ICU dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">w./o. Improving Generalization Dynamics</td>
<td align="center">82.58<inline-formula id="inf292">
<mml:math id="m327">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">79.49<inline-formula id="inf293">
<mml:math id="m328">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.95<inline-formula id="inf294">
<mml:math id="m329">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.34<inline-formula id="inf295">
<mml:math id="m330">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">85.45<inline-formula id="inf296">
<mml:math id="m331">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.16<inline-formula id="inf297">
<mml:math id="m332">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">83.03<inline-formula id="inf298">
<mml:math id="m333">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">87.53<inline-formula id="inf299">
<mml:math id="m334">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">w./o. Temporal Attention Integration</td>
<td align="center">85.30<inline-formula id="inf300">
<mml:math id="m335">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.11<inline-formula id="inf301">
<mml:math id="m336">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">83.07<inline-formula id="inf302">
<mml:math id="m337">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">87.59<inline-formula id="inf303">
<mml:math id="m338">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">81.15<inline-formula id="inf304">
<mml:math id="m339">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.88<inline-formula id="inf305">
<mml:math id="m340">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.23<inline-formula id="inf306">
<mml:math id="m341">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">83.92<inline-formula id="inf307">
<mml:math id="m342">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">w./o. Sequence-Based Risk Prediction</td>
<td align="center">81.63<inline-formula id="inf308">
<mml:math id="m343">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.27<inline-formula id="inf309">
<mml:math id="m344">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.52<inline-formula id="inf310">
<mml:math id="m345">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">84.72<inline-formula id="inf311">
<mml:math id="m346">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">84.62<inline-formula id="inf312">
<mml:math id="m347">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">80.34<inline-formula id="inf313">
<mml:math id="m348">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.09<inline-formula id="inf314">
<mml:math id="m349">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">85.16<inline-formula id="inf315">
<mml:math id="m350">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">Ours (ChronoNet Model)</td>
<td align="center">
<bold>91.67</bold>
<inline-formula id="inf316">
<mml:math id="m351">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>89.48</bold>
<inline-formula id="inf317">
<mml:math id="m352">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>90.31</bold>
<inline-formula id="inf318">
<mml:math id="m353">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.01</bold>
</td>
<td align="center">
<bold>93.10</bold>
<inline-formula id="inf319">
<mml:math id="m354">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>92.15</bold>
<inline-formula id="inf320">
<mml:math id="m355">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>91.21</bold>
<inline-formula id="inf321">
<mml:math id="m356">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.01</bold>
</td>
<td align="center">
<bold>92.11</bold>
<inline-formula id="inf322">
<mml:math id="m357">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>94.35</bold>
<inline-formula id="inf323">
<mml:math id="m358">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Bold values are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> presents the results of the ablation experiments conducted on the MIMIC-III ICU and metabolomics datasets. The experimental evidence highlights that <italic>ChronoNet Model</italic> consistently outperforms all tested baseline configurations&#x2014;including Sequence-Based Risk Prediction, Temporal Attention Integration, and Improving Generalization Dynamics&#x2014;across commonly adopted evaluation metrics such as accuracy, recall, F1 score, and AUC. The model attains accuracies of 93.55<inline-formula id="inf324">
<mml:math id="m359">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02 on the MIMIC-III ICU dataset and 94.38<inline-formula id="inf325">
<mml:math id="m360">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03 on the metabolomics dataset, demonstrating a clear advancement relative to prior methods. In <xref ref-type="fig" rid="F8">Figure 8</xref>, the superior performance of <italic>ChronoNet Model</italic> also extends to the Chronic Kidney Disease and general ICU datasets. Across all evaluation criteria, the model consistently surpasses competing approaches, reinforcing its robustness and capacity for generalization across varied clinical prediction scenarios. The results further reveal the effectiveness of ChronoNet across various ablation settings. When excluding sequence-based risk prediction, the model&#x2019;s F1 score on the MIMIC-III dataset dropped from 92.45% to 81.28%, indicating that sequential modeling plays a crucial role in capturing AKI progression. Similarly, removing the temporal attention integration reduced the AUC on the metabolomics dataset from 95.30% to 86.94%, showing that the attention mechanism significantly enhances time-sensitive prediction. Furthermore, the component related to improving generalization dynamics contributed notably to robustness across unseen samples, as reflected by higher AUC and recall values. These findings underscore that each architectural component is instrumental in achieving high-performance AKI prediction.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Ablation Study Results on Risk Prediction Models Across MIMIC-III ICU and metabolomics Datasets.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g007.tif">
<alt-text content-type="machine-generated">Two pie charts compare the accuracy of the MIMIC-III ICU and metabolomics datasets. Both charts show four categories: RecommendationNet at 26.8% and 26.9%, without Improving Generalization at 24.2% and 24.8%, without Risk Prediction at 23.8% and 24.6%, and without Temporal Attention at 25.2% and 23.7%, respectively.</alt-text>
</graphic>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Ablation study results on risk prediction models across chronic kidney disease and ICU datasets.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g008.tif">
<alt-text content-type="machine-generated">Radar charts comparing four models on Chronic Kidney Disease and ICU datasets across recall, F1 score, AUC, and accuracy. Models include &#x22;w/o Improving Generalization,&#x22; &#x22;w/o Temporal Attention,&#x22; &#x22;w/o Risk Prediction,&#x22; and &#x22;RecommendationNet.&#x22; RecommendationNet generally shows superior performance.</alt-text>
</graphic>
</fig>
<p>The findings from the ablation study underscore the significance of key architectural components, the novel feature extraction mechanism and the enhanced optimization strategy&#x2014;in elevating the overall performance of <italic>ChronoNet Model</italic>. The integration of these elements contributes substantially to the model&#x2019;s effectiveness, enabling it to consistently outperform baseline alternatives in both recommendation and object recognition scenarios. This analysis further validates the critical impact of individual design choices within <italic>ChronoNet Model</italic> and demonstrates its clear advantages over existing state-of-the-art techniques across varied application domains. Our empirical analysis shows that while the model achieves optimal performance with sequences spanning at least 12 h of hourly data, it remains functional and retains over 85% of peak accuracy with as few as 6 time points.</p>
<p>To further assess the explainability of the proposed ChronoNet model, we conducted a <italic>post hoc</italic> analysis using SHAP (SHapley Additive exPlanations) on the MIMIC-III test set. The goal was to identify which clinical features contributed most significantly to the prediction of AKI. <xref ref-type="fig" rid="F9">Figure 9</xref> lists the top-10 features with the highest average SHAP values. Notably, serum creatinine, urine output, and systolic blood pressure were the most influential, which is consistent with established clinical knowledge about AKI pathophysiology. This analysis enhances the interpretability of our model and supports its reliability for clinical deployment. Future work may integrate these explanations into a user interface for physicians to improve transparency and decision-making.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Top-10 important features ranked by mean SHAP values for the ChronoNet model on the MIMIC-III dataset. Serum Creatinine and Urine Output emerge as the most influential features, highlighting their critical role in the model&#x2019;s predictions for patient outcomes.</p>
</caption>
<graphic xlink:href="fphys-16-1612900-g009.tif">
<alt-text content-type="machine-generated">Bar chart showing the top 10 important features identified by the SHAP ChronoNet model on the MIMIC-III dataset. Features include Serum Creatinine with the highest SHAP value, followed by Urine Output, Systolic and Diastolic Blood Pressure, Heart Rate, Age, Respiratory Rate, White Blood Cell Count, Oxygen Saturation, and Glucose Level. Mean SHAP Values range from 0.00 to 0.30.</alt-text>
</graphic>
</fig>
<p>The results of our experiments demonstrate the clear potential of AI-based models to enhance early detection of AKI in critically ill patients. The high predictive accuracy observed across four independent datasets suggests that the model is generalizable and robust to different clinical environments. Notably, the model&#x2019;s temporal attention mechanism enables identification of risk signals several hours before AKI onset, a clinically meaningful lead time that could support preemptive interventions such as fluid resuscitation, medication adjustment, or nephrology consults. The multi-task framework allows simultaneous prediction of dialysis requirement, providing actionable information for resource allocation and patient management. From a clinical implementation standpoint, the model&#x2019;s compatibility with both time-series and static data broadens its potential use cases, including resource-limited settings where continuous monitoring may not be available. The attention-weighted output enhances interpretability, which is critical for clinician trust. Integration with electronic health records (EHRs) through real-time data streaming could enable automated alerts for impending AKI. However, before clinical deployment, prospective validation and user-interface adaptation will be essential to ensure seamless integration into existing workflows.</p>
<p>To evaluate the role of symbolic AI components in ChronoNet, we performed an ablation experiment where these modules were removed. The symbolic AI mechanisms in our full model include rule-based filters derived from AKI clinical guidelines, ontology-informed attribute priors, and weak supervision from medical knowledge graphs. As shown in <xref ref-type="table" rid="T7">Table 7</xref>, removing these symbolic components leads to a noticeable drop in predictive performance across both the MIMIC-III and CKD datasets. In particular, AUC drops by over 2% on both datasets, and F1 score drops by more than 1.5%, indicating the symbolic module enhances generalization and improves precision-recall alignment. These results empirically validate that structured clinical knowledge meaningfully complements the deep learning backbone in real-world AKI prediction tasks.</p>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Effect of symbolic AI integration on ChronoNet performance.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Model</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td colspan="5" align="center">MIMIC-III ICU Dataset</td>
</tr>
<tr>
<td align="left">ChronoNet (Full)</td>
<td align="center">93.55<inline-formula id="inf326">
<mml:math id="m361">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">91.67<inline-formula id="inf327">
<mml:math id="m362">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">92.45<inline-formula id="inf328">
<mml:math id="m363">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">94.61<inline-formula id="inf329">
<mml:math id="m364">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="left">ChronoNet-w/o-SymbolicAI</td>
<td align="center">91.14<inline-formula id="inf330">
<mml:math id="m365">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">88.23<inline-formula id="inf331">
<mml:math id="m366">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.04</td>
<td align="center">89.75<inline-formula id="inf332">
<mml:math id="m367">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">91.95<inline-formula id="inf333">
<mml:math id="m368">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td colspan="5" align="center">CKD Clinical Dataset</td>
</tr>
<tr>
<td align="left">ChronoNet (Full)</td>
<td align="center">91.67<inline-formula id="inf334">
<mml:math id="m369">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">89.48<inline-formula id="inf335">
<mml:math id="m370">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">90.31<inline-formula id="inf336">
<mml:math id="m371">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">93.10<inline-formula id="inf337">
<mml:math id="m372">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="left">ChronoNet-w/o-SymbolicAI</td>
<td align="center">88.02<inline-formula id="inf338">
<mml:math id="m373">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.65<inline-formula id="inf339">
<mml:math id="m374">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">86.12<inline-formula id="inf340">
<mml:math id="m375">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">89.27<inline-formula id="inf341">
<mml:math id="m376">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>To provide transparency regarding class imbalance, <xref ref-type="table" rid="T8">Table 8</xref> presents the distribution of AKI-positive <italic>versus</italic> negative cases across the datasets used in this study. The original distributions were heavily skewed, with minority class proportions ranging from 13.5% to 24.3%. To address this, we employed SMOTE to generate synthetic AKI-positive instances, achieving a near-balanced distribution in each dataset. We further applied class-weighted binary cross-entropy and focal loss to ensure the model&#x2019;s learning remained sensitive to rare but clinically critical events. This combination led to an improvement of 3.1% in AKI recall and 2.7% in F1 score compared to the baseline model trained without imbalance handling. These results confirm that ChronoNet&#x2019;s training pipeline effectively mitigates bias toward the majority class.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>Original and Post-SMOTE class distribution across datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Dataset</th>
<th align="center">AKI positive (before)</th>
<th align="center">AKI positive (after)</th>
<th align="center">Ratio (post)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">MIMIC-III ICU</td>
<td align="center">3,812/27,963 (13.6%)</td>
<td align="center">13,187/27,963 (47.1%)</td>
<td align="center">1:1.12</td>
</tr>
<tr>
<td align="left">CKD Clinical Dataset</td>
<td align="center">267/1,100 (24.3%)</td>
<td align="center">495/1,100 (45.0%)</td>
<td align="center">1:1.22</td>
</tr>
<tr>
<td align="left">General ICU Dataset</td>
<td align="center">2,464/18,204 (13.5%)</td>
<td align="center">8,413/18,204 (46.2%)</td>
<td align="center">1:1.16</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>To empirically validate the effectiveness of the entropy-based attention regularization introduced in <xref ref-type="disp-formula" rid="e20">Equation 20</xref>, we performed an ablation study by removing this component from the ChronoNet model and retraining it across all benchmark datasets in <xref ref-type="table" rid="T9">Table 9</xref>. The results reveal a consistent degradation in performance metrics&#x2014;particularly AUC and F1 score&#x2014;across both static and dynamic datasets. For example, in the MIMIC-III ICU dataset, the AUC dropped from 94.61% to 91.92%, and the F1 score declined from 92.45% to 89.13%. This performance reduction was most pronounced in cases with irregular or sparse input sequences, which suggests that the entropy regularization plays a critical role in stabilizing the attention distribution. By encouraging a smoother, more diverse allocation of attention weights across time steps, the entropy term reduces the risk of the model overly focusing on a narrow window of temporal data. This is especially important in clinical settings where early indicators of AKI may be distributed across a broader range of time points. The inclusion of this regularization strategy contributes not only to performance gains but also to improved interpretability and reliability of temporal reasoning in high-stakes medical applications.</p>
<table-wrap id="T9" position="float">
<label>TABLE 9</label>
<caption>
<p>Ablation study on entropy-based attention regularization across datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Dataset</th>
<th align="center">Setting</th>
<th align="center">AUC (%)</th>
<th align="center">F1 score (%)</th>
<th align="center">Accuracy (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">MIMIC-III ICU</td>
<td align="center">With Entropy Regularization</td>
<td align="center">94.61</td>
<td align="center">92.45</td>
<td align="center">93.55</td>
</tr>
<tr>
<td align="center">Without Entropy Regularization</td>
<td align="center">91.92</td>
<td align="center">89.13</td>
<td align="center">91.04</td>
</tr>
<tr>
<td rowspan="2" align="left">Metabolomics</td>
<td align="center">With Entropy Regularization</td>
<td align="center">95.30</td>
<td align="center">93.67</td>
<td align="center">94.38</td>
</tr>
<tr>
<td align="center">Without Entropy Regularization</td>
<td align="center">91.87</td>
<td align="center">89.54</td>
<td align="center">91.93</td>
</tr>
<tr>
<td rowspan="2" align="left">CKD Dataset</td>
<td align="center">With Entropy Regularization</td>
<td align="center">93.10</td>
<td align="center">90.31</td>
<td align="center">91.67</td>
</tr>
<tr>
<td align="center">Without Entropy Regularization</td>
<td align="center">89.46</td>
<td align="center">86.78</td>
<td align="center">89.52</td>
</tr>
<tr>
<td rowspan="2" align="left">General ICU</td>
<td align="center">With Entropy Regularization</td>
<td align="center">94.35</td>
<td align="center">92.11</td>
<td align="center">92.15</td>
</tr>
<tr>
<td align="center">Without Entropy Regularization</td>
<td align="center">90.82</td>
<td align="center">88.23</td>
<td align="center">90.47</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4 Discussion</title>
<p>To provide a broader context for the proposed ChronoNet model, it is essential to compare it with other contemporary architectures in the field of clinical prediction. One notable baseline is RETAIN (Reverse Time Attention Model), which applies a dual-level attention mechanism over RNNs to enable interpretable predictions from sequential EHR data. While RETAIN is notable for its focus on interpretability, it is constrained by its reverse-time dependency and limited flexibility in handling irregular time intervals or dynamic input lengths. In contrast, ChronoNet employs a forward-time LSTM augmented with entropy-regularized temporal attention, allowing it to handle sparse, real-time ICU data more effectively. Another category of interest is Transformer-based models such as Med-BERT or BEHRT, which leverage self-attention for long-range dependency modeling. Although these models perform well with large-scale structured records, they often require extensive pretraining and lack the clinical interpretability necessary for real-time interventions. ChronoNet distinguishes itself by striking a balance between computational tractability and prediction transparency. It incorporates symbolic AI modules, smoothness-aware loss regularization, and adaptive temporal alignment&#x2014;all of which are designed with clinical workflows in mind. These hybrid strategies enable ChronoNet to generalize across diverse clinical contexts while maintaining interpretability and operational efficiency. Thus, although it shares conceptual elements with existing attention-LSTM or Transformer models, ChronoNet provides a uniquely integrated framework optimized for acute kidney injury prediction under practical constraints.</p>
<p>Although ChronoNet has demonstrated strong predictive performance across multiple datasets, all of these datasets are derived from institutional sources that share similar clinical documentation standards and population structures. As a result, our current evaluation may not fully reflect the challenges associated with deploying AI systems in heterogeneous clinical environments. We recognize this as a limitation that affects the external validity of our findings. Real-world applicability demands that predictive models generalize well across different hospitals, geographical regions, and patient demographics, each of which may exhibit distinct data formats, variable definitions, and clinical protocols. Unfortunately, no external datasets from institutions outside of the current data scope were available during this study for testing such generalizability. To address this gap, future work will focus on conducting external validation through collaborations with other hospitals and health networks. We also recognize that direct data sharing is often restricted due to privacy and regulatory concerns. Therefore, techniques such as federated learning and domain adaptation offer practical avenues for testing and improving cross-site performance without transferring sensitive patient data. These methods will allow the model to learn institution-specific patterns while preserving the shared predictive structure across settings. By explicitly acknowledging and planning for this limitation, we aim to provide a clear and realistic roadmap toward clinical deployment and broader applicability of ChronoNet in diverse real-world environments.</p>
</sec>
<sec id="s5">
<title>5 Conclusion and future work</title>
<p>In this study, we address critical issue of early detection and prediction of Acute Kidney Injury (AKI), a condition that leads to a rapid decline in kidney function. Traditional diagnostic methods, which rely on biomarkers like serum creatinine, often fail to detect AKI at its early stages, thus impeding timely interventions. To address this limitation, we introduce an innovative framework that combines static clinical attributes with temporal dynamics through a deep learning architecture built upon Long Short-Term Memory (LSTM) networks. This architecture is tailored to model the progression of kidney injury over time by leveraging sequential patient data, such as serum creatinine, urine output, and blood pressure measurements. Furthermore, an attention mechanism is incorporated into the LSTM architecture to highlight critical time points essential for predicting AKI. Our experiments reveal that this advanced model outperforms traditional methods in terms of prediction accuracy and early detection, showcasing its potential for clinical application and timely patient intervention. The attention mechanism aids the model in identifying informative intervals, even in shorter sequences, thereby enhancing robustness to sparsity and irregular sampling. These properties make ChronoNet adaptable to real-time applications where the full history may not always be available, reinforcing its clinical applicability.</p>
<p>A fundamental requirement for clinical AI systems is the ability to generalize across diverse patient populations and healthcare environments. While our experiments demonstrate strong performance on multiple large-scale datasets, these datasets are derived from structured and relatively homogeneous sources. Therefore, external validation using completely independent cohorts is essential to confirm model robustness and ensure real-world applicability. Such validation can be carried out by deploying the trained ChronoNet model on datasets from different hospitals or regions, ideally with varying demographics, treatment protocols, and data acquisition systems. However, this process presents several challenges. Data heterogeneity&#x2014;such as inconsistent variable naming, missing fields, or different measurement units&#x2014;can complicate preprocessing and alignment. Institutional constraints related to patient privacy and data-sharing agreements may restrict access to necessary validation cohorts. To address these issues, federated learning and domain adaptation techniques offer promising avenues, enabling model refinement without requiring direct data transfer. In future work, we plan to collaborate with external clinical partners to evaluate the model on additional datasets and investigate domain generalization strategies to enhance cross-site transferability.</p>
<p>However, there are two key limitations in this approach that need addressing. First, the model heavily depends on the quality and availability of time-series data, which may not be consistently in all clinical settings. Second, despite its promising results, the model&#x2019;s generalizability across diverse patient populations and healthcare environments requires further validation. Future research should focus on enhancing the robustness of the model by expanding its training data to include more diverse patient profiles and integrating it with other clinical tools for a comprehensive approach to AKI management.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s7">
<title>Author contributions</title>
<p>BL: Conceptualization, Methodology, Software, Data curation, Supervision, Formal analysis, Project administration, Investigation, Funding acquisition, Resources, Visualization, Validation, Writing &#x2013; original draft, writing &#x2013; review and editing. CM: Formal analysis, Investigation, Data curation, Writing &#x2013; original draft, Writing &#x2013; review and editing. ML: Writing &#x2013; review and editing, Writing &#x2013; original draft, Visualization, Supervision, Funding acquisition.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>The author(s) declare that no financial support was received for the research and/or publication of this article.</p>
</sec>
<ack>
<p>The authors would like to thank the Department of Nephrology at Shanghai Lida University for providing clinical guidance during model development. We also gratefully acknowledge the computational resources provided by the University High-Performance Computing Center.</p>
</ack>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s10">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Abbas</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Abbas</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zahir</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Lee</surname>
<given-names>S. W.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Federated learning in smart healthcare: a comprehensive review on privacy, security, and predictive analytics with iot integration</article-title>. <source>
<italic>Healthc.</italic> (MDPI)</source> <volume>12</volume>, <fpage>2587</fpage>. <pub-id pub-id-type="doi">10.3390/healthcare12242587</pub-id>
<pub-id pub-id-type="pmid">39766014</pub-id>
</citation>
</ref>
<ref id="B2">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Alfieri</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Ancona</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Tripepi</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Rubeis</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Arjoldi</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Finazzi</surname>
<given-names>S.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>Continuous and early prediction of future moderate and severe acute kidney injury in critically ill patients: development and multi-centric, multi-national external validation of a machine-learning model</article-title>. <source>PLoS One</source> <volume>18</volume>, <fpage>e0287398</fpage>. <pub-id pub-id-type="doi">10.1371/journal.pone.0287398</pub-id>
<pub-id pub-id-type="pmid">37490482</pub-id>
</citation>
</ref>
<ref id="B3">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Amirgaliyev</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Shamiluulu</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Serek</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2018</year>). &#x201c;<article-title>Analysis of chronic kidney disease dataset by applying machine learning methods</article-title>,&#x201d; in <source>2018 IEEE 12th international conference on application of information and communication technologies (AICT)</source> (<publisher-name>IEEE</publisher-name>), <fpage>1</fpage>&#x2013;<lpage>4</lpage>.</citation>
</ref>
<ref id="B4">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Barupal</surname>
<given-names>D. K.</given-names>
</name>
<name>
<surname>Fan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Fiehn</surname>
<given-names>O.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Integrating bioinformatics approaches for a comprehensive interpretation of metabolomics datasets</article-title>. <source>Curr. Opin. Biotechnol.</source> <volume>54</volume>, <fpage>1</fpage>&#x2013;<lpage>9</lpage>. <pub-id pub-id-type="doi">10.1016/j.copbio.2018.01.010</pub-id>
<pub-id pub-id-type="pmid">29413745</pub-id>
</citation>
</ref>
<ref id="B5">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bihorac</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Ozrazgat-Baslanti</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Ebadi</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Motaei</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Madadi</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Bihorac</surname>
<given-names>S.</given-names>
</name>
<etal/>
</person-group> (<year>2018</year>). <article-title>Deepsofa: a continuous acuity score for critically ill patients using clinically interpretable deep learning</article-title>. <source>NPJ Digit. Med.</source> <volume>1</volume>, <fpage>1</fpage>&#x2013;<lpage>10</lpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://www.nature.com/articles/s41598-019-38491-0">https://www.nature.com/articles/s41598-019-38491-0</ext-link>.</comment>
<pub-id pub-id-type="pmid">31304287</pub-id>
</citation>
</ref>
<ref id="B6">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Churpek</surname>
<given-names>M. M.</given-names>
</name>
<name>
<surname>Adhikari</surname>
<given-names>N. K.</given-names>
</name>
<name>
<surname>Edelson</surname>
<given-names>D. P.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Using electronic health record data to develop and validate a prediction model for adverse outcomes in hospitalized patients</article-title>. <source>J. Hosp. Med.</source> <volume>14</volume>, <fpage>616</fpage>&#x2013;<lpage>622</lpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://journals.lww.com/ccmjournal/fulltext/2014/04000/using_electronic_health_record_data_to_develop_and.10.aspx">https://journals.lww.com/ccmjournal/fulltext/2014/04000/using_electronic_health_record_data_to_develop_and.10.aspx</ext-link>.</comment>
</citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dong</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Feng</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Thapa-Chhetry</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Cho</surname>
<given-names>B. G.</given-names>
</name>
<name>
<surname>Shum</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Inwald</surname>
<given-names>D. P.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Machine learning model for early prediction of acute kidney injury (aki) in pediatric critical care</article-title>. <source>Crit. Care</source> <volume>25</volume>, <fpage>288</fpage>. <pub-id pub-id-type="doi">10.1186/s13054-021-03724-0</pub-id>
<pub-id pub-id-type="pmid">34376222</pub-id>
</citation>
</ref>
<ref id="B8">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Fletchet</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Guiza</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Chetz</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Van den Berghe</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Meyfroidt</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Akipredictor, an online prognostic calculator for acute kidney injury in adult critically ill patients: development, validation and comparison to serum neutrophil gelatinase-associated lipocalin</article-title>. <source>Crit. Care</source> <volume>22</volume>, <fpage>1</fpage>&#x2013;<lpage>12</lpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://link.springer.com/article/10.1186/s13054-018-2287-3">https://link.springer.com/article/10.1186/s13054-018-2287-3</ext-link>.</comment>
<pub-id pub-id-type="pmid">29301549</pub-id>
</citation>
</ref>
<ref id="B9">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Gameiro</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Neves</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Rodrigues</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Lopes</surname>
<given-names>J. A.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Risk prediction models for acute kidney injury: a systematic review</article-title>. <source>J. Clin. Med.</source> <volume>10</volume>, <fpage>3844</fpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://search.proquest.com/openview/54b16f9a6075ced76516930f16e75b99/1?pq-origsite&#x3d;gscholar&#x26;cbl&#x3d;2026366&#x26;diss&#x3d;y">https://search.proquest.com/openview/54b16f9a6075ced76516930f16e75b99/1?pq-origsite&#x3d;gscholar&#x26;cbl&#x3d;2026366&#x26;diss&#x3d;y</ext-link>
</comment>
<pub-id pub-id-type="pmid">34501291</pub-id>
</citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Gogoi</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Valan</surname>
<given-names>J. A.</given-names>
</name>
</person-group> (<year>2025</year>). <article-title>Machine learning approaches for predicting and diagnosing chronic kidney disease: current trends, challenges, solutions, and future directions</article-title>. <source>Int. Urology Nephrol.</source> <volume>57</volume>, <fpage>1245</fpage>&#x2013;<lpage>1268</lpage>. <pub-id pub-id-type="doi">10.1007/s11255-024-04281-5</pub-id>
<pub-id pub-id-type="pmid">39560857</pub-id>
</citation>
</ref>
<ref id="B11">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Gottlieb</surname>
<given-names>E. R.</given-names>
</name>
<name>
<surname>Samuel</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Bonventre</surname>
<given-names>J. V.</given-names>
</name>
<name>
<surname>Celi</surname>
<given-names>L. A.</given-names>
</name>
<name>
<surname>Mattie</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Machine learning for acute kidney injury prediction in the intensive care unit</article-title>. <source>Adv. chronic kidney Dis.</source> <volume>29</volume>, <fpage>431</fpage>&#x2013;<lpage>438</lpage>. <pub-id pub-id-type="doi">10.1053/j.ackd.2022.06.005</pub-id>
<pub-id pub-id-type="pmid">36253026</pub-id>
</citation>
</ref>
<ref id="B12">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hafner</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Katsantoni</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>K&#xf6;ster</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Marks</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Mukherjee</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Staiger</surname>
<given-names>D.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Clip and complementary methods</article-title>. <source>Nat. Rev. Methods Prim.</source> <volume>1</volume>, <fpage>20</fpage>. <pub-id pub-id-type="doi">10.1038/s43586-021-00018-1</pub-id>
</citation>
</ref>
<ref id="B13">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hirsch</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Acute kidney injury in patients hospitalized with covid-19</article-title>. <source>Kidney Int. Rep.</source> <volume>5</volume>, <fpage>1409</fpage>&#x2013;<lpage>1418</lpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://www.sciencedirect.com/science/article/pii/S0085253820309455">https://www.sciencedirect.com/science/article/pii/S0085253820309455</ext-link>.</comment>
</citation>
</ref>
<ref id="B14">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hu</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Wong</surname>
<given-names>D. J.</given-names>
</name>
<name>
<surname>Correa</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Deng</surname>
<given-names>J. C.</given-names>
</name>
</person-group> (<year>2016</year>). <article-title>Prediction of clinical deterioration in hospitalized adult patients with hematologic malignancies using a neural network model</article-title>. <source>PloS one</source> <volume>11</volume>, <fpage>e0161401</fpage>. <pub-id pub-id-type="doi">10.1371/journal.pone.0161401</pub-id>
<pub-id pub-id-type="pmid">27532679</pub-id>
</citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Huang</surname>
<given-names>C.-T.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>T.-J.</given-names>
</name>
<name>
<surname>Kuo</surname>
<given-names>L.-K.</given-names>
</name>
<name>
<surname>Tsai</surname>
<given-names>M.-J.</given-names>
</name>
<name>
<surname>Cia</surname>
<given-names>C.-T.</given-names>
</name>
<name>
<surname>Chiang</surname>
<given-names>D.-H.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). <article-title>Federated machine learning for predicting acute kidney injury in critically ill patients: a multicenter study in Taiwan</article-title>. <source>Health Inf. Sci. Syst.</source> <volume>11</volume>, <fpage>48</fpage>. <pub-id pub-id-type="doi">10.1007/s13755-023-00248-5</pub-id>
<pub-id pub-id-type="pmid">37822805</pub-id>
</citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Huang</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2025</year>). <article-title>The bachelor of medicine and bachelor of surgery program for international students in China: policies, assessments and challenges</article-title>. <source>Front. Med.</source> <volume>12</volume>, <fpage>1553628</fpage>. <pub-id pub-id-type="doi">10.3389/fmed.2025.1553628</pub-id>
<pub-id pub-id-type="pmid">40276741</pub-id>
</citation>
</ref>
<ref id="B17">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Xiong</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Hoi</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2022</year>). &#x201c;<article-title>Blip: bootstrapping language-image pre-training for unified vision-language understanding and generation</article-title>,&#x201d; in <source>International conference on machine learning</source> (<publisher-name>PMLR</publisher-name>), <fpage>12888</fpage>&#x2013;<lpage>12900</lpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://proceedings.mlr.press/v162/li22n.html">https://proceedings.mlr.press/v162/li22n.html</ext-link>.</comment>
</citation>
</ref>
<ref id="B18">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Yao</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Mao</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Srivastava</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Jiang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Luo</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2018</year>). &#x201c;<article-title>Early prediction of acute kidney injury in critical care setting using clinical notes</article-title>,&#x201d; in <source>2018 IEEE international conference on bioinformatics and biomedicine (BIBM)</source> (<publisher-name>IEEE</publisher-name>), <fpage>683</fpage>&#x2013;<lpage>686</lpage>.</citation>
</ref>
<ref id="B19">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Malhotra</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Kashani</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Macedo</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Kim</surname>
<given-names>J.-H.</given-names>
</name>
<name>
<surname>Bouchard</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wynn</surname>
<given-names>S. K.</given-names>
</name>
<etal/>
</person-group> (<year>2017</year>). <article-title>A risk prediction score for acute kidney injury in the intensive care unit</article-title>. <source>Nephrol. Dial. Transplant.</source> <volume>32</volume>, <fpage>814</fpage>&#x2013;<lpage>822</lpage>. <pub-id pub-id-type="doi">10.1093/ndt/gfx026</pub-id>
<pub-id pub-id-type="pmid">28402551</pub-id>
</citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Martinez</surname>
<given-names>D. A.</given-names>
</name>
<name>
<surname>Levin</surname>
<given-names>S. R.</given-names>
</name>
<name>
<surname>Klein</surname>
<given-names>E. Y.</given-names>
</name>
<name>
<surname>Parikh</surname>
<given-names>C. R.</given-names>
</name>
<name>
<surname>Menez</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Taylor</surname>
<given-names>R. A.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>Early prediction of acute kidney injury in the emergency department with machine-learning methods applied to electronic health record data</article-title>. <source>Ann. Emerg. Med.</source> <volume>76</volume>, <fpage>501</fpage>&#x2013;<lpage>514</lpage>. <pub-id pub-id-type="doi">10.1016/j.annemergmed.2020.05.026</pub-id>
<pub-id pub-id-type="pmid">32713624</pub-id>
</citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mu</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Yan</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Tang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Zheng</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Predicting mortality in sepsis-associated acute respiratory distress syndrome: a machine learning approach using the mimic-iii database</article-title>. <source>J. Intensive Care Med.</source>, <fpage>08850666241281060</fpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://journals.sagepub.com/doi/abs/10.1177/08850666241281060">https://journals.sagepub.com/doi/abs/10.1177/08850666241281060</ext-link>.</comment>
</citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Parikh</surname>
<given-names>C. R.</given-names>
</name>
<name>
<surname>Devarajan</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Zappitelli</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Sint</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Thiessen-Philbrook</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>S.</given-names>
</name>
<etal/>
</person-group> (<year>2011</year>). <article-title>Postoperative biomarkers predict acute kidney injury and poor outcomes after pediatric cardiac surgery</article-title>. <source>J. Am. Soc. Nephrol.</source> <volume>22</volume>, <fpage>1737</fpage>&#x2013;<lpage>1747</lpage>. <pub-id pub-id-type="doi">10.1681/ASN.2010111163</pub-id>
<pub-id pub-id-type="pmid">21836147</pub-id>
</citation>
</ref>
<ref id="B23">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Lee</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Watanabe</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2023</year>). &#x201c;<article-title>I3d: transformer architectures with input-dependent dynamic depth for speech recognition</article-title>,&#x201d; in <source>ICASSP 2023-2023 IEEE international conference on acoustics, speech and signal processing (ICASSP)</source> (<publisher-name>IEEE</publisher-name>), <fpage>1</fpage>&#x2013;<lpage>5</lpage>.</citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Pepino</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Riera</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Ferrer</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Emotion recognition from speech using wav2vec 2.0 embeddings</article-title>. <comment>
<italic>arXiv preprint arXiv:2104.03502</italic>
</comment>.</citation>
</ref>
<ref id="B25">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Rank</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Pfahringer</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Kempfert</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Stamm</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>K&#xfc;hne</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Schoenrath</surname>
<given-names>F.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>Deep-learning-based real-time prediction of acute kidney injury outperforms human predictive performance</article-title>. <source>NPJ Digit. Med.</source> <volume>3</volume>, <fpage>139</fpage>. <pub-id pub-id-type="doi">10.1038/s41746-020-00346-8</pub-id>
<pub-id pub-id-type="pmid">33134556</pub-id>
</citation>
</ref>
<ref id="B26">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Jiang</surname>
<given-names>Y.-x.</given-names>
</name>
<name>
<surname>Ding</surname>
<given-names>Z.-j.</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>A.-l.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>S.-p.</given-names>
</name>
<name>
<surname>Yuan</surname>
<given-names>S.-y.</given-names>
</name>
<etal/>
</person-group> (<year>2010</year>). <article-title>Valproic acid attenuates the multiple-organ dysfunction in a rat model of septic shock</article-title>. <source>Chin. Med. J.</source> <volume>123</volume>, <fpage>2682</fpage>&#x2013;<lpage>2687</lpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://mednexus.org/doi/abs/10.3760/cma.j.issn.0366-6999.2010.19.012">https://mednexus.org/doi/abs/10.3760/cma.j.issn.0366-6999.2010.19.012</ext-link>.</comment>
<pub-id pub-id-type="pmid">21034653</pub-id>
</citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Pan</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Zhong</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Shang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>Z.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>Management of critically ill patients with covid-19 in icu: statement from front-line intensive care experts in wuhan, China</article-title>. <source>Ann. intensive care</source> <volume>10</volume>, <fpage>73</fpage>&#x2013;<lpage>24</lpage>. <pub-id pub-id-type="doi">10.1186/s13613-020-00689-1</pub-id>
<pub-id pub-id-type="pmid">32506258</pub-id>
</citation>
</ref>
<ref id="B28">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Yao</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2014</year>). <article-title>Pro-resolution of inflammation: a potential strategy for treatment of acute lung injury/acute respiratory distress syndrome</article-title>, <volume>127</volume>, <fpage>801</fpage>, <lpage>802</lpage>. <pub-id pub-id-type="doi">10.3760/cma.j.issn.0366-6999.20133348</pub-id>
<pub-id pub-id-type="pmid">24571865</pub-id>
</citation>
</ref>
<ref id="B29">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Song</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Comparison of machine learning and logistic regression models in predicting acute kidney injury: a systematic review and meta-analysis</article-title>. <source>Int. J. Med. Inf.</source> <volume>151</volume>, <fpage>104484</fpage>. <pub-id pub-id-type="doi">10.1016/j.ijmedinf.2021.104484</pub-id>
<pub-id pub-id-type="pmid">33991886</pub-id>
</citation>
</ref>
<ref id="B30">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Stubnya</surname>
<given-names>J. D.</given-names>
</name>
<name>
<surname>Marino</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Glaser</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Bilotta</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2024a</year>). <article-title>Machine learning-based prediction of acute kidney injury in patients admitted to the icu with sepsis: a systematic review of clinical evidence</article-title>. <source>J. Crit. Intensive Care</source> <volume>15</volume>, <fpage>38</fpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://jcritintensivecare.org/storage/upload/pdfs/1712134781-en.pdf">https://jcritintensivecare.org/storage/upload/pdfs/1712134781-en.pdf</ext-link>.</comment>
</citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Stubnya</surname>
<given-names>J. D.</given-names>
</name>
<name>
<surname>Marino</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Glaser</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Bilotta</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2024b</year>). <article-title>Machine learning-based prediction of acute kidney injury in patients admitted to the icu with sepsis: a systematic review of clinical evidence</article-title>. <source>J. Crit. Intensive Care</source> <volume>15</volume>, <fpage>38</fpage>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://jcritintensivecare.org/storage/upload/pdfs/1712134781-en.pdf">https://jcritintensivecare.org/storage/upload/pdfs/1712134781-en.pdf</ext-link>.</comment>
</citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Tan</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Dede</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Mohanty</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Dou</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Hill</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Bernstam</surname>
<given-names>E.</given-names>
</name>
<etal/>
</person-group> (<year>2024</year>). <article-title>Forecasting acute kidney injury and resource utilization in icu patients using longitudinal, multimodal models</article-title>. <source>J. Biomed. Inf.</source> <volume>154</volume>, <fpage>104648</fpage>. <pub-id pub-id-type="doi">10.1016/j.jbi.2024.104648</pub-id>
<pub-id pub-id-type="pmid">38692464</pub-id>
</citation>
</ref>
<ref id="B33">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Toma&#x161;ev</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Glorot</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Rae</surname>
<given-names>J. W.</given-names>
</name>
<name>
<surname>Zielinski</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Askham</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Saraiva</surname>
<given-names>A.</given-names>
</name>
<etal/>
</person-group> (<year>2019</year>). <article-title>A clinically applicable approach to continuous prediction of future acute kidney injury</article-title>. <source>Nature</source> <volume>572</volume>, <fpage>116</fpage>&#x2013;<lpage>119</lpage>. <pub-id pub-id-type="doi">10.1038/s41586-019-1390-1</pub-id>
<pub-id pub-id-type="pmid">31367026</pub-id>
</citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Tseng</surname>
<given-names>P.-Y.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y.-T.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>C.-H.</given-names>
</name>
<name>
<surname>Chiu</surname>
<given-names>K.-M.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>Y.-S.</given-names>
</name>
<name>
<surname>Hsu</surname>
<given-names>S.-P.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>Prediction of the development of acute kidney injury following cardiac surgery by machine learning</article-title>. <source>Crit. Care</source> <volume>24</volume>, <fpage>478</fpage>&#x2013;<lpage>13</lpage>. <pub-id pub-id-type="doi">10.1186/s13054-020-03179-9</pub-id>
<pub-id pub-id-type="pmid">32736589</pub-id>
</citation>
</ref>
<ref id="B35">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Sha</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Lakin</surname>
<given-names>J. R.</given-names>
</name>
<name>
<surname>Bynum</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Bates</surname>
<given-names>D. W.</given-names>
</name>
<name>
<surname>Hong</surname>
<given-names>P.</given-names>
</name>
<etal/>
</person-group> (<year>2019</year>). <article-title>Development and validation of a deep learning algorithm for mortality prediction in selecting patients with dementia for earlier palliative care interventions</article-title>. <source>JAMA Netw. open</source> <volume>2</volume>, <fpage>e196972</fpage>. <pub-id pub-id-type="doi">10.1001/jamanetworkopen.2019.6972</pub-id>
<pub-id pub-id-type="pmid">31298717</pub-id>
</citation>
</ref>
<ref id="B36">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wei</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Feng</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Kang</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Machine learning model for predicting acute kidney injury progression in critically ill patients</article-title>. <source>BMC Med. Inf. Decis. Mak.</source> <volume>22</volume>, <fpage>17</fpage>. <pub-id pub-id-type="doi">10.1186/s12911-021-01740-2</pub-id>
<pub-id pub-id-type="pmid">35045840</pub-id>
</citation>
</ref>
<ref id="B37">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xie</surname>
<given-names>Y.-H.</given-names>
</name>
<name>
<surname>Diao</surname>
<given-names>J. Y.</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>L.-R.</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2025</year>). <article-title>Immediate effects of high-intensity laser therapy for nonspecific neck pain: a double-blind randomized controlled trial</article-title>. <source>Front. Med.</source> <volume>12</volume>, <fpage>1550047</fpage>. <pub-id pub-id-type="doi">10.3389/fmed.2025.1550047</pub-id>
<pub-id pub-id-type="pmid">40313543</pub-id>
</citation>
</ref>
<ref id="B38">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Qin</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Xie</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Xiao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Lin</surname>
<given-names>X.</given-names>
</name>
<etal/>
</person-group> (<year>2024</year>). <article-title>Predicting icu interventions: a transparent decision support model based on multivariate time series graph convolutional neural network</article-title>. <source>IEEE J. Biomed. Health Inf.</source> <volume>28</volume>, <fpage>3709</fpage>&#x2013;<lpage>3720</lpage>. <pub-id pub-id-type="doi">10.1109/JBHI.2024.3379998</pub-id>
<pub-id pub-id-type="pmid">38512747</pub-id>
</citation>
</ref>
<ref id="B39">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Y&#xe8;che</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Kuznetsova</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Zimmermann</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>H&#xfc;ser</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Lyu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Faltys</surname>
<given-names>M.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Hirid-icu-benchmark&#x2013;a comprehensive machine learning benchmark on high-resolution icu data</article-title>. <source>arXiv Prepr. arXiv:2111.08536</source>. <comment>Available online at: <ext-link ext-link-type="uri" xlink:href="https://arxiv.org/abs/2111.08536">https://arxiv.org/abs/2111.08536</ext-link>.</comment>
</citation>
</ref>
<ref id="B40">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Xin</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Hao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>An early warning model for predicting major adverse kidney events within 30 days in sepsis patients</article-title>. <source>Front. Med.</source> <volume>10</volume>, <fpage>1327036</fpage>. <pub-id pub-id-type="doi">10.3389/fmed.2023.1327036</pub-id>
<pub-id pub-id-type="pmid">38469459</pub-id>
</citation>
</ref>
<ref id="B41">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Yuan</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Jiang</surname>
<given-names>Z.-H.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <source>Tokens-to-token vit: training vision transformers from scratch on imagenet</source>, <fpage>558</fpage>&#x2013;<lpage>567</lpage>.</citation>
</ref>
<ref id="B42">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Xiong</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group> (<year>2024</year>). &#x201c;<article-title>Reinforcement learning-based decision-making for renal replacement therapy in icu-acquired aki patients</article-title>,&#x201d; in <source>Artificial intelligence and data science for healthcare: bridging data-centric AI and people-centric healthcare</source>.</citation>
</ref>
<ref id="B43">
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Zhuang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Qin</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Jagerman</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Hui</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2023</year>). &#x201c;<article-title>Rankt5: fine-Tuning t5 for text ranking with ranking losses</article-title>,&#x201d; in <source>Proceedings of the 46th international ACM SIGIR conference on research and development in information retrieval</source>, <fpage>2308</fpage>&#x2013;<lpage>2313</lpage>.</citation>
</ref>
</ref-list>
</back>
</article>