“Things are linked by invisible ties, you cannot pick a flower without disturbing a star.” – Galileo Galilei.

Throughout the centuries, humanity has consistently sought to find connections between various phenomena to uncover underlying universal principles. This desire for cohesion has driven scientific research and philosophical reflection, with historical examples such as the ancient Greeks’ interest in the arché and Newton’s laws unifying celestial and terrestrial motion. The search for a “theory of everything” in physics represents the latest effort to unite all the fundamental forces and particles of the universe into a single formulation (Hawking, 2006; Huang et al., 2018; Kirk et al., 1983; Wilson, 1999).

Despite the desire to uncover unifying principles, progress in this area has been limited, primarily due to the lack of adequate theoretical and computational tools (Holland, 1995; Mitchell, 2009). However, in recent decades, significant changes have occurred. The rise of interdisciplinary collaboration across scientific fields has fostered a powerful synergy, advancing innovative theoretical frameworks and computational methodologies. The complex systems approach, central to this development, focuses on understanding the interactions and emergent behaviors of system components rather than isolating them (Parisi, 1999; Ladyman et al., 2013; Estrada, 2024). This contrasts with the reductionist method, which seeks to explain phenomena by breaking them down into their smallest parts. While reductionism excels in studying individual components, the complex systems approach abstracts fundamental principles governing diverse systems, regardless of context, providing deeper and more unified models (Denning, 2017; Zorzo et al., 2024).

In this scenario, two foundational tools - network science (NS) and machine learning (ML) - have the potential, when effectively integrated, to significantly advance the discovery of shared principles across diverse domains. NS focuses on studying complex systems modeled as networks, which consist of nodes (representing entities or elements) and edges (representing the connections or relationships between nodes). This framework allows us to analyze the structure, dynamics, and behavior of interconnected systems across various fields. By representing entities and their interactions as nodes and edges, network science enables researchers to apply graph theory to reveal common patterns and principles that transcend individual disciplines (Iñiguez et al., 2020; Das and Soylu, 2023). For example, it has been applied across a wide range of domains—including materials science, cosmology, social sciences, biology, and technology—to analyze phenomena such as phase transitions, information flow, disease transmission, social dynamics, and technological innovation (Patel et al., 2024; Choudhary and DeCost, 2021; Batzner et al., 2022; Aroboto et al., 2023; Batatia et al., 2025; Strey et al., 2023; Artime et al., 2024; Pósfai and Barabási, 2016; Rosato et al., 2008). ML is a key aspect of Artificial Intelligence (AI), enabling systems to perform tasks requiring human-like intelligence, such as learning and problem-solving. ML could help researchers to extract insights from diverse data, uncovering hidden patterns and potential universal principles across various fields. It enables the automated discovery of correlations, associations, and causal relationships, facilitating cross-domain comparisons (Khetani et al., 2023; Longo et al., 2024). This paper focuses on Explainable ML systems (XML) as they offer several key advantages, including greater transparency, enabling users to understand model decisions and build trust (Angelini et al., 2024; D’Amore et al., 2024; Islam et al., 2022; Linardatos et al., 2020; Guidotti et al., 2019b; Bodria et al., 2023). XML ability to analyze feature importance is especially valuable for comparing different domains. NS and XML offer complementary approaches for studying shared principles across different domains through computer simulations and big data analytics. By integrating these methodologies, researchers can harness the strengths of each to address interdisciplinary challenges, uncover hidden patterns, and deepen our understanding of complex systems in science and beyond.

This article introduces a highly interdisciplinary methodological approach that, for the first time, combines NS and XML to explore the possibility of uncovering shared organizational and functional principles across scientific domains. As an example, it discusses how the methodology could be applied to four seemingly unrelated areas: atomic structures in materials science, neuroscience, social science, and cosmology. These four domains were chosen because they represent distinct yet fundamental scales of organization, ranging from the microscopic to the cosmic. By examining atomic structures, we gain insights into the fundamental building blocks of matter. Neuroscience allows us to explore complex biological systems and cognitive processes. Social science offers a lens into the behavior of human networks, while cosmology extends our understanding to the vast structures of the universe. Despite their differences, these domains could share underlying patterns and principles that reveal universal organizational dynamics, making them ideal for comparative analysis. The study focuses on criticality, a crucial concept for understanding how complex systems transition between states, why they exhibit sudden shifts in behavior, and how universal patterns emerge across different scales. Criticality, a phenomenon extensively studied, serves as a representative phenomenon for analyzing the dynamics of complex systems.

The integration of NS and XML could represent a significant methodological advancement, offering new insights into cross-domain similarities that have not been previously explored in the literature. By applying this approach, the paper seeks to go beyond existing studies and provide a deeper understanding of the fundamental organizational principles shared across these domains, thus offering both a fresh research perspective and new contributions to the field. The significance of our research lies in its potential to foster unprecedented collaboration across disciplinary boundaries, paving the way for innovative discoveries. A key advantage of identifying common principles across domains is the use of transfer learning, an ML technique that adapts models from one domain to another, reducing the need for extensive training data (Pan and Yang, 2009; Weiss et al., 2016). In cases where data collection is challenging, such as in the observation of cosmic phenomena, transfer learning can exploit similarities between complex systems to enhance the efficiency of training. The proposed approach could also offer practical benefits by advancing theoretical understanding and enabling cross-domain applications. Insights from one field can inspire breakthroughs in another. For example, connections between atomic structures and brain activity might lead to advanced neurotechnology materials, while parallels between social and cosmic networks could inform models of collective behavior, impacting fields like sociology and astrophysics.

Criticality refers to continuous (second-order) phase transitions, where a system undergoes a smooth but profound change in state characterized by diverging correlation lengths, scale invariance, and critical fluctuations. This is distinct from first-order transitions, which involve abrupt changes and latent heat, such as melting or boiling. Criticality occurs across fields, such as in materials science, where, near critical temperature or pressure, small fluctuations can cause significant changes, such as the emergence of superconductivity or superfluidity, showcasing criticality role in material behavior (Stanley, 1971; Nishimori and Ortiz, 2011; Petrucci et al., 2017; Parisi et al., 2017; Fultz, 2020). In neuroscience, phase transitions occur in neural dynamics, such as shifts between unconscious and conscious states or non-REM and REM sleep (Allegrini et al., 2015). Criticality emerges when small disturbances in neural networks cause large-scale changes, driving cognitive or brain state shifts. Alterations in criticality, rather than its complete loss, are linked to neurodegenerative disorders, where deviations from optimal critical states disrupt brain function (Beggs and Plenz, 2003; Beggs, 2008; Chialvo, 2010). In social science, phase transitions occur during sudden societal shifts or market changes, such as rapid smartphone adoption or financial crises, where small fluctuations in behavior or confidence trigger large transformations (Levy, 2005; Contucci et al., 2008; Fukami and Nakajima, 2011). In cosmic science, phase transitions include events like the early universe cooling after the Big Bang or gas clouds collapsing into stars. Criticality is key in these processes, where small energy density fluctuations near critical points shape the universe’s structure, influencing galaxy and star formation (Guardo et al., 2014; Barrow and Scherrer, 2018).

Criticality offers a powerful lens to explore interconnected phenomena across scales, from atoms to the brain, society, and the cosmos. It marks tipping points where systems undergo transformative changes, uncovering universal principles that govern complex behaviors. From atomic reorganization and neural shifts to societal changes and cosmic events, criticality shows how small fluctuations can trigger large-scale effects, revealing fundamental mechanisms that link diverse domains.

This section introduces a five-steps computational method for quantitatively analyzing the mechanisms governing criticality across materials science, neuroscience, social sciences, and cosmology. Figure 1 shows the proposed framework. The procedure is explained with theoretical and computational justifications for the choices made and examples illustrating its application to specific cases. While the method is applied to the case of criticality in this work, it is general and can be extended to investigate other shared phenomena.

The practical implementation of the proposed methodology involves several key technical aspects that warrant detailed discussion, particularly regarding the selection of graph metrics, the scalability of XML models, and the computational cost of transfer learning across domains.

The proposed framework aims to generalize across disciplines, but a brief comparison with traditional methods used in each example domain helps clarify its distinct contribution. In materials science, conventional studies of phase transitions often rely on atomistic simulations—such as molecular dynamics or Monte Carlo methods—or thermodynamic models. While these offer high-fidelity representations, they are computationally intensive and tailored to specific physical systems (Tavenner et al., 2023; Łach, 2025). Abstracting material systems as interaction networks could enable the detection of structural patterns associated with critical behavior in a more generalizable and scalable form. Crucially, combining NS with XML could enhance this framework by providing not only predictive capabilities but also interpretability. XML models could identify which network features most influence phase behavior, offering insights that are both actionable and transferable across materials. This synergy could facilitate the development of lightweight, interpretable tools that complement traditional simulations while broadening the scope for cross-domain generalization. Brain activity is typically analyzed using statistical and signal processing techniques such as spectral analysis, dynamic causal modeling, or multivariate pattern analysis. While these methods yield valuable insights into specific neural processes, they seldom capture system-level organization or dynamics associated with criticality (Razi and Friston, 2016; Bahrami et al., 2023). The proposed approach shifts focus toward modeling brain function as a complex network, using graph-based features that characterize large-scale connectivity patterns. When combined with XML, this representation could enable interpretable analyses that highlight which structural properties most influence emergent neural behavior. This integrative methodology may support cross-domain generalization and contribute to identifying potential common principles underlying critical dynamics in both biological and artificial systems. Social systems are often explored through statistical models, agent-based simulations, or qualitative analysis. While NS has gained traction in this domain, its application typically remains confined to specific tasks such as community detection or information diffusion (Borgatti et al., 2009; Weisburd et al., 2024). The proposed framework takes a broader approach by leveraging generalizable graph features to enable structural comparisons across domains and identify shared patterns underlying complex social behaviors. By integrating NS with XML, the methodology may support predictive modeling while offering insights into which topological properties are most likely to influence system dynamics. This combination could enable interpretable and scalable analyses that extend beyond isolated use cases, potentially facilitating the identification of shared principles across social and other complex systems. Finally, large-scale simulations of the universe—such as N-body or lattice field models—serve as the standard tools for studying cosmic structure and phase transitions. These simulations are grounded in physical laws but do not typically support interpretability or cross-domain comparison (Bertschinger, 1998; Partmann et al., 2020). Representing cosmological systems as graphs may help identify structural markers (e.g., critical points) that resemble patterns observed in other complex systems. In addition, combining NS with XML could offer added interpretability and potential for generalization. While NS can highlight topological signatures of complex dynamics, XML techniques might help trace how specific features contribute to model predictions. This integrated approach may support hypothesis generation across domains and promote transparency—an important consideration when modeling phenomena as intricate and data-intensive as cosmology. From this comparative perspective, the proposed methodology has the potential to shift the focus from domain-specific optimization toward uncovering shared mechanisms—such as criticality—through unified NS representations and XML-based analysis.

This section highlights the potential benefits of identifying common principles across domains, which may enable transfer learning—a machine learning technique that adapts a model trained in one domain for use in a related one. This approach could potentially reduce training time and resource demands, especially when data is limited. For instance, recognizing critical states in cosmic systems with sparse data could be facilitated by first training a model on more accessible neuroscience data. Transfer learning would then adapt the model for application in cosmology, helping it detect critical states in less monitored systems.

Beyond this example, the proposed framework could provide a structured approach for identifying analogies between phenomena in seemingly unrelated fields. Detecting similar patterns of criticality through graph metrics—such as phase transitions in materials and neural activity in the brain—could help generate hypotheses about how structural features shape functional behavior across systems. These cross-domain parallels could potentially offer a foundation for designing interfaces that better align with the brain natural dynamics, enhancing both adaptability and performance. The key connection lies in the shared dynamics of criticality observed across domains, which could, for example, inform the design of neuroprosthetic devices by enhancing their timing and responsiveness. In this respect, studying how materials undergo phase transitions that alter electrical conductivity near critical points may support the development of biocompatible materials optimized for stable and efficient neural interfaces. Feature importance analysis can help identify the structural or functional properties that most influence criticality in both materials and neural networks. By manipulating these key features, it may become possible to modulate critical behavior in both systems, thereby enhancing the efficiency and stability of interactions between engineered materials and the brain, particularly near critical thresholds. Within this framework, causal AI could explore how properties like flexibility and biocompatibility influence neuroprosthetic integration near critical thresholds. Meanwhile, correlational AI could detect links between material microstructure and electrical performance, and in neuroscience, between material characteristics and neural tissue compatibility. Overall, these integrated insights could support the co-design of materials and devices tailored for reliable performance at key points of interaction. More broadly, the same approach could be extended to other domains—such as linking behavioral tipping points in society with neural state transitions, or comparing stress propagation in engineered structures with energy distribution during cosmological phase transitions—to leverage shared principles of criticality. This could enable a deeper understanding of how complex behaviors emerge and stabilize across fields.

This paper explores an interdisciplinary, system-level approach that could potentially be used to uncover common principles across different scientific domains. As an example, the paper focuses on materials science, neuroscience, social science, and cosmology, with an emphasis on criticality. It combines NS and XML to propose a five-step method: gathering relational data, converting it into a neutral framework, building graph-based datasets, using XML to compare criticality across fields, and applying findings back to specific domains. This approach could potentially enable XML models to work in fields with limited data, such as applying neuroscience insights to detect critical states in cosmology.

In the future, extending explainability by incorporating rule-based and counterfactual-based explanations could enhance model interpretability, especially in complex domains (Guidotti et al., 2019a; Guidotti et al., 2021). This would broaden the scope beyond feature importance methods and shift towards a more comprehensive Explainable AI (XAI) framework, offering more intuitive and actionable insights, thus increasing transparency and trust across various applications (Samek et al., 2019; Guidotti et al., 2024). Additionally, exploring the integration of explainable machine learning (XML) techniques with graph-based neural networks—such as Graph Convolutional Networks and Graph Attention Networks—may offer valuable insights. Such a comparison could clarify trade-offs between interpretability and performance, and inform hybrid strategies that effectively balance explanatory depth with predictive accuracy (Khemani et al., 2024; Li et al., 2024).

By integrating NS and XML, the proposed framework offers a structured and interpretable approach for cross-domain analysis. While this study focused on four exemplary domains—materials science, neuroscience, social science, and cosmology—and on the phenomenon of criticality, the methodology is generalizable and designed to accommodate other scientific areas and complex phenomena. In particular, it can be extended to investigate additional emergent behaviors, such as synchronization, resilience, and adaptation, which are prevalent in many natural and artificial systems (Holland, 1992; Bar-Yam, 2002; Siegenfeld and Bar-Yam, 2020; Artime et al., 2024). Shared properties across domains—such as hierarchical organization, feedback loops, and nonlinear dynamics—give rise to complex behaviors including crystallization in materials, neural synchronization in the brain, and structure formation in the cosmos. Recognizing and systematically comparing these patterns through a unified analytical lens could drive breakthroughs not only in neurotechnology and materials science, but also in fields like ecology, epidemiology, and economics, ultimately fostering both theoretical insight and practical innovation through interdisciplinary collaboration. Future research will focus on implementing and testing the framework on real-world datasets (Strey et al., 2023; Failla et al., 2024; Ohana et al., 2024; The Multimodal Universe Collaboration et al., 2025; Batatia et al., 2025). Initial experiments on selected domain-specific data could provide evidence of practical performance and manageable computational requirements. However, quantitative benchmarking across diverse datasets, systematic performance evaluation, and scalability testing will be essential to validate the framework robustness and generalizability. For example, comparing the model ability to identify critical states against established benchmarks—such as known phase transition models in materials science or cosmological simulations—could help assess the scientific validity of the detected patterns. This next phase will be key to establishing the practical viability of the approach in applied scientific and engineering contexts.