The chemical and biochemical industries face numerous challenges and opportunities due to the ever-changing technological landscape. The rise of Industry 4.0 and Industry 5.0, as presented in Figure 1, has brought about digitalization and automation, offering the potential for significant efficiency and productivity improvements. As presented in Figure 2, companies can improve operations and transition to Industry 4.0 and 5.0 by employing advanced technologies such as Digital Twins (DTs), Internet of Things (IoT), Artificial Intelligence (AI), and big data analytics, among others (Udugama et al., 2021; Gargalo et al., 2021; Pandey et al., 2024; Isoko et al., 2024). Indeed, Industry 4.0 is the embodiment of digital transformation through the development of high-fidelity digital copies of the processing plant operations (Gargalo et al., 2021; Isoko et al., 2024). Although Industries 4.0 and 5.0 both leverage advanced technologies (see Figure 2), the former is focused mainly on automation and digital transformation towards smart manufacturing, whereas the latter targets improving the collaboration between humans and machines towards a more “human-centric” approach (Aheleroff et al., 2022; Maddikunta et al., 2022; Nahavandi, 2019). Moreover, while Industry 4.0 paves the way for a sustainable (bio)economy, Industry 5.0 emphasizes and implements the concept of circularity (Pandey et al., 2024). Adopting circular (bio)economy leads companies to reduce, reuse, and recycle by leveraging technologies like IoT sensors for continuous energy monitoring, AI-powered analytics, and additive manufacturing. This paradigm targets to reconcile technological advancements with human values (“human-centric”), sustainability and environmental-conscious decision-making (aiming to reduce the environmental impact in place since the rise of Industry 2.0), and workforce well-being, promoting agile and robust production systems (Aheleroff et al., 2022; Bazel et al., 2024; He and Chand, 2024; Maddikunta et al., 2022).

Yet, the journey towards successful implementation of Industry 4.0 in (bio)chemical processing plants is not simple and/or straightforward (Pandey et al., 2024; Isoko et al., 2024; Udugama et al., 2021). It implies not only technological advancements but also workforce training, organizational changes, and regulatory backing (Pandey et al., 2024; Isoko et al., 2024; Udugama et al., 2021; Gargalo et al., 2021). In particular, the biochemical industry, including sectors such as enzyme production and biopharma, seems to be falling behind, with many companies still operating within the limitations of Industry 3.0 (Arden et al., 2021). This gap can be due to various reasons, including the intrinsic complexity of biological systems (difficult to optimize and scale), regulatory guidelines, scalability, data security, and the high expenses linked with upgrading current infrastructure (e.g., sensors, cloud computing, cybersecurity) (Isoko et al., 2024; Gargalo et al., 2021; Arden et al., 2021; Maddikunta et al., 2022). Another significant barrier to the digitalization of the (bio) industry is the shortage of skilled workforce - digital literacy is now a mandatory set of skills (Caccavale et al., 2024). Thus, the adoption of Education 4.0 in educational institutions is under discussion, with some Universities taking the lead in training students towards this goal (Caccavale et al., 2024).

Despite these and other challenges companies face in implementing Industry 4.0 principles in the chemical and biochemical industries, several technologies have emerged that could facilitate the implementation of these strategies. Hybrid modelling is a promising approach that combines first-principles models with the flexibility of data-driven techniques to make more accurate predictions, improving process control and optimization, and increasing efficiency and flexibility (Narayanan et al., 2023; Sokolov et al., 2021; Narayanan et al., 2020; Albino et al., 2024). Hybrid models work on counteracting the advantages/disadvantages of both mechanistic and data-driven approaches. This synergy not only improves the predictive accuracy of models but also provides deeper insights into process dynamics, enabling better control and optimization (Narayanan et al., 2020; Narayanan et al., 2023). This approach is especially applicable and beneficial for industries where data generation is highly resource intensive, and the fundamental processes are not 100% understood (e.g., biochemical processes, transport and reaction mechanisms) (Narayanan et al., 2023; Yu et al., 2022). This is due to the fact that hybrid modelling identifies a compromise between the governing relationships among the variables while permitting the flexibility to discover possible interactions between these variables (Narayanan et al., 2023). Therefore, in essence, one substitutes excessively intricate processes that cannot be physically modelled with simplified dynamic, machine learning (ML) processes, or time series modelling. This enables the direct acquisition of new parameterizations from observations and/or high-resolution model simulations using machine ML methods (Kasilingam et al., 2024). Even before coining the term of hybrid modelling in 1992 (Psichogios and Ungar, 1992), numerous works on grey box modeling have demonstrated their successful implementation in representing complex systems, such as, for example, kinetic modelling (e.g., Monod), mass transfer between liquid and gas phases, among others. In summary, the shift toward Industry 4.0 and 5.0 brings both challenges and opportunities for the chemical and biochemical industries. Although the journey ahead may be challenging, the potential benefits in terms of efficiency, improved sustainability, and competitiveness are too significant to overlook. We believe that this article will shed light on these challenges and motivate further research and discussion.

The remaining manuscript is organized as follows. Section 2 delves deeper into concepts and principles behind the successful implementation of hybrid modelling, and discusses the advantages over conventional modelling approaches in the context of Industries 4.0 and 5.0. Section 3 presents a pragmatic review of works detailing the implementation of hybrid modelling and discusses the lessons learned. Section 4 presents perspectives on the use of hybrid modelling for resource optimization and the pursuit of sustainability. Lastly, Section 5 summarizes the main findings and provides insights for future advancements in this field.

As previously mentioned, we distinguish between two distinct modelling approaches: i) knowledge-driven, and ii) data-driven. Combining these two results in a third approach, a hybrid modelling approach. Each approach will be elaborated on in this section so as to provide the rationale for the emergence of hybrid modelling.

Knowledge-based modelling is also referred to as mechanistic modelling, first-principles modelling, white-box modelling, parametric modelling, or physics/science-based modelling. Despite the wide range of terminologies used, the concurring fact is that such an approach is based on a first-principles understanding of the phenomena occurring in the system, where the parameters in the model have a physical meaning. Such models include physical laws and constraints resulting from combining observations, theoretical analysis, hypothesis construction, and experimental validation (Rudolph et al., 2024). These laws usually result in mass, energy, and momentum conservation laws. First principle models conventionally take the form of either algebraic equations, systems of ordinary differential equations (ODEs), or systems of partial differential equations (PDEs).

Many studies have focused on the mechanistic modelling of various processes relating to the upstream and downstream of chemical and biochemical industries. Some examples are: Saccharomyces cerevisiae fermentation process (Sonnleitner and Käppeli, 1986), lactic acid bacteria fermentation (Spann et al., 2018), filamentous fungal fermentation (Mears et al., 2017), membrane filtration (Rischawy et al., 2023), pectin extraction (Andersen et al., 2017), ion exchange chromatography (Rischawy et al., 2022; Meyer et al., 2023) and distillation processes (Bisgaard et al., 2017).

Mechanistic models are usually data-efficient (in contrast to data-hungry) and are capable of providing a causal explanation of the generated output. As such, they are reliable as long as the underlying assumptions and the domain of applicability are valid. One major drawback of this modelling approach is that it requires expert domain knowledge to derive the underlying dynamics. Considering the multiscale nature of many of the phenomena occurring in a chemical process and the wide range of expertise required (metabolism, metagenomics, fluid dynamics, etc.), this could pose a serious challenge. This a challenge many have sought to solve using data-driven modelling.

Data-driven modelling is also referred to as black-box modelling and non-parametric modelling. The concept of nonparametric reflects the fact that the parameters in these models do not carry any physically meaningful sense. These models are data-centric and use the data to deduce the underlying patterns between a set of inputs and outputs. This pattern recognition is used to approximate the underlying mechanism, which is especially important when the true dynamics are too complex for to derive first-principles models. Data-driven modelling is usually based either on statistical modelling or more recently on ML principles. Statistical modelling has been used for many years, e.g., the use of autoregressive and moving average models for time series, linear multivariate models (partial least square model), as well as non-linear multivariable models (polynomial functions). The major distinction between ML-based models and statistical or classical first-principles models is that the relationship between the input and output is not explicitly programmed or encoded in the program. ML covers a wide range of modelling techniques that can be classified based on the model structure, the learning process, or the intended application. Model structures include deep neural networks, Gaussian processes, graph neural networks, support vector machines, random forests, k-nearest neighbors, etc. Intended applications include regression (predicting numerical values), classification (predicting classes), or clustering (group data based on similarity). The learning process covers supervised (data used are labeled) and unsupervised learning (data used are not labeled).

The strength of data-driven models is that they do not “require” expert domain knowledge and are capable of extracting highly non-linear relationships between the input and output. This is especially the case for deep neural networks, which, in theory, are capable of approximating any non-linear function (hence the universal approximation nature). However, data-driven models are data inefficient (data “hungry”) as the data demand scales exponentially with the feature dimensions (Schweidtmann et al., 2023). This results in over-parameterized models (with many weights), which ultimately results in overfitting, especially if the number of parameters exceeds that of the data used for model training. Furthermore, the nonparametric models lack an aspect of explainability, meaning that despite the ability to capture the intricate relationships between input and output, they cannot explain the underlying mechanism of a given system, thus the black-box notation. A model’s ability to extrapolate is of great interest regardless of the underlying modelling approach. Mechanistic models are well suited for extrapolation (as long as the assumptions hold) and the limits of the models can be subjected to analysis. Meanwhile, some data-driven techniques such as deep neural networks are subject to the universal approximation principle and can in theory replicate any non-linear continuous trend. However, the validity of these models when subjected to extreme values is not well described but can be inferred through simulation.

Efforts to alleviate the weaknesses of both modelling approaches while leveraging their individual strengths gave birth to the concept of hybrid modelling. As such, a hybrid model is any model that combines first-principles and data-centric approaches. These models are also referred to as semi-parametric, as only a subset of its parameters carries any physical meaning. Hybrid models can potentially provide high accuracies while maintaining a certain degree of interpretability. The work by Psichogios and Ungar (1992) as highlighted by Schweidtmann et al. (2023) reported an improved model performance through better extrapolation, a reduced need for data, and an increased interpretability of the models. However, hybrid modelling could also pose a new challenge as such approaches require both expertise and knowledge in first-principles modelling and data-driven modelling to ensure efficient integration Rudolph et al. (2024). Such an added layer of complexity can arise in determining the level of detail of each compartment and a suitable configuration to combine the two approaches.

Rudolph et al. (2024) provide an extensive overview of hybrid models design patterns. These design patterns are generalized to unify and formalize the various modelling approaches across domains and applications. These design patterns are introduced in the following and exemplified by a few selected relevant studies from the literature. A more extensive list can be found in Section 3 (dissection and analysis of case studies). Rudolph et al. (2024) defined two types of hybrid modelling design patterns based on how the parametric and the non-parametric models interact into base patterns and composition patterns. The base patterns cover basic elemental units and take two computational models (one parametric and one non-parametric). These base patterns cover the delta model, physics-based preprocessing, feature learning, and physical constraints (soft and hard constraints). The delta model is identical to what Psichogios and Ungar (1992) and von Stosch et al. (2014) refer to as the parallel structure. This design pattern aims to use the same input for both models and combine their output into the final target through, e.g., summation. This is especially useful when the mechanistic model is not entirely understood nor capable of capturing the entire dynamics exhibited by the system. Therefore, the data-driven part compensates for this lack of details in the mechanistic model, yielding higher accuracy and robustness. An example could be that the mechanistic part describes an ideal system with a set of associated assumptions, while the data-driven model provides corrective action to overcome these assumptions. Bradley et al. (2022) also refer to this as “mechanism correction”. As such, an important distinction of this configuration is that the two models are, in principle, “independent” of each other, and the sole functionality of the data-driven model is to “improve” and “correct” the performance of the mechanistic model. An advantage of the delta model configuration is that it is less data dependent, as modelling residuals of the mechanistic model is easier than modelling the complete dynamics of the system and thus will require less data than a complete data-driven model. From a conceptual point of view, this configuration supports “specialization”. The delta model is capable of overcoming cases where it is infeasible for data to be obtained abundantly over the entire input space (expensive, safety, or time-consuming). For data beyond the training domain (aka the test set), the mechanistic model allows for safe extrapolation, while for data already considered in the training domain, the data-driven model is already “specialized” as it offers accurate and reliable predictions. One disadvantage of this approach is that it does not allow for higher-order interactions between the two blocks, as their output is only added together. Besides the parallel combination of the two modelling approaches, combining these sequentially (serial model structure) is also possible. For this, Rudolph et al. (2024) distinguishes between two types of serial combinations based on their purpose: “physics-based preprocessing” or “feature learning”, depending on the relative positions of the mechanistic and data-driven model.

If the data-driven approach processes the data-driven model, it is called “feature learning”. This pattern is used when the mechanistic model requires input that might be either difficult or infeasible to measure directly, and thus, the need for the data-driven model to infer these from auxiliary measurements or inputs. Within this pattern, we further distinguish between two “learning paradigms”: sequential and end-to-end learning. In sequential learning, the training of the two models is decoupled. This can be used when the desired feature or input to the mechanistic model is available but at much less frequency or size than the other measurements. Then, a data-driven model can be trained using a set of inputs to predict this correctly. The output of this can then be used in the mechanistic model. In end-to-end learning, the training of the models is combined, and the two models are jointly optimized using, e.g., backpropagation of the errors and gradient-based algorithms. This, however, requires both models to be differentiable, which is always the case for the data-driven model, but in some cases, the derivative of the mechanistic model can be non-tractable. In both cases, the main advantage is that the output of the hybrid model is still physically constrained by the mechanistic part, increasing its reliability. State estimators for control systems are a perfect example of this approach.

In the “physics-based preprocessing” design pattern, domain knowledge is used to perform a set of transformations to produce a set of inputs that can support and enhance the performance of the data-driven model. This reduces the resources allocated by the data-driven model for feature extraction, making it easier to relate the input to the output. This is especially true as the risk of learning irrelevant features is avoided. This also potentially reduces the need for complex architecture and long training time. This inductive bias reduces the input data dimensionality and can enhance accuracy and interpretability. However, it is important to note that in some cases and due to the “representation learning capabilities” of data-driven models, they might be capable of extracting better underlying features than humans. This renders the mechanistic part an obstacle rather than an advantage.

The final base pattern defined by Rudolph et al. (2024) is the physically constrained hybrid approach. These constraints can affect the parameters, structure, or output of the hybrid model. As such, two types of constraints are introduced: soft and hard constraints. The mechanistic part of this pattern is not necessarily a model but can also be domain knowledge. The difference is that hard constraints cannot be violated, while soft constraints exhibit some elasticity that occasionally allows them to be breached. The previously described feature learning pattern is comparable to a hard constraint design pattern but ultimately differs in the aim and purpose, while the physics-informed neural network is an example of a soft constraint design pattern. An example of a hard constraint could be the addition of a ReLU layer at the end of a neural network to ensure that the output is non-negative to model concentrations and pressure or using a softmax layer to ensure output is between zero and one for molar fractions (Aouichaoui et al., 2023). An important prerequisite for the hard constraint modelling approach is that the data used are in fact in line with said constraint. This corrective action is also known as data reconciliation. A major challenge with introducing hard constraints is that it might result in non-differentiable models making it harder to use gradient-based optimization (Rudolph et al., 2024).

In soft-constrained design, the mechanistic insight is incorporated into the loss function as a penalty to guide the data-driven model toward fulfilling the domain knowledge during training. The aim is that this constraint is somehow retained at inference time, and therefore, at inference, the model is purely data-driven, where knowledge is implicitly encoded. An example of such an approach includes physics-informed neural networks (PINNs). These models have been heavily used in problems that include differential and partial differential equations. These models introduce an additional term to the loss function of the neural network that reflects the dynamics that occur in the system. This term usually reflects the “initial and boundary conditions along the space-time domins as well as the residuals of the (partial) differential equation system” (Cuomo et al., 2022). It is important to note that this adds an additional challenge to the modelling process as the objective function now becomes multi-objective, which will then require calibration in order to balance the two target objectives. Another potential issue arises, such models might not be able to catch complex dynamics that present multi-scale behaviours (Cuomo et al., 2022).

Finally, these base design patterns can be combined in many ways to create composition patterns. Two patterns are defined: recurrent composition and hierarchical composition. The recurrent composition involves models that are updated using an internal state. This update can either be in the form of a data-driven model or a mechanistic model. The recurrent pattern is similar to recurrent neural networks and numerical integration for differential equations. The advantage of this composite pattern is that it enables pattern recognition across time and parameter sharing (the same parameters are used for all time steps). This parameter sharing will then result in a model with a reduced number of parameters and resulting in a model with a global understanding of the dynamics of the system. The hierarchical pattern composition consists of combining two or more distinct hybrid modelling patterns. This allows modelling for more complex problems. An example would be to apply a delta pattern to two distinct hybrid models, each trained with soft constraints in the form of domain knowledge in the loss function. Figure 3 revisits the advantages of white-, gray- (hybrid modelling), and black-box modelling, while Figure 4 presents an overview of the various base design patterns along with their advantages and disadvantages.

As previously mentioned, hybrid modelling has gained increased interest from the modelling and digitalization communities within the biochemical industry, combining the strengths of mechanistic and data-driven modelling paradigms to address the complexities inherent in various biological processes. This review examines 50 case studies published between 2020 and 2024, providing a comprehensive analysis of the principles, challenges, and lessons learned from the application of hybrid modelling across a range of biochemical processes. This comprehensive review is presented in Supplementary Table S1. Of the 50 case studies reviewed, a significant proportion (28) dealt with fermentation and bioprocesses, 12 on downstream processes, eight on upstream chemical processes, and two on the holistic chemical processes. A schematic overview of the analyzed case studies is presented in Supplementary Figure S1. In this figure, the case studies are categorized and examined based on the year of publication, citation count, the process investigated, and the hybrid model pattern used.

Industries are under increasing pressure to adapt, innovate, and strike a balance between environmental accountability and economic prosperity (highlighted by the Green Deal (European Commission, 2019)). The digital transformation is a paramount element in achieving the goals set by the Green Deal (Garske et al., 2024; Bauer et al., 2021; European Commission, 2020), and of note is that the sustainability and sustainable and digital transition are intertwined in a myriad of ways (Garske et al., 2024; Ekardt, 2022).

The digital transition paradigm aims at streamlining and improving accessibility by converting analog information into digital platforms. The changing landscape, marked by evolving regulations, customer demands, and environmental considerations, is currently challenging conventional processes and standards. The drive towards implementing Industry 4.0, and even 5.0, offers an excellent opportunity (and challenges) to address these concerns and ensure positive steps towards increased sustainability in all regards; thus, it plans for social welfare, economic growth, and positive environmental impact (three pillars of sustainability). This section, as illustrated in Figure 5, explores the interplay/relationships between digitalization, hybrid modelling, and sustainability and the opportunities they hold for the future of manufacturing.

Several concepts have arisen as key drivers of efficiency and sustainability in this fast-evolving technological paradigm. A crucial example is, as previously mentioned, the concept of digital twins (DTs), virtual copies of entire running physical production plants, processes and/or supply chains. DTs allow for real-time monitoring and control, predictive analytics and scenario simulation, optimization, and predictive maintenance, among others. DTs enable organizations to pinpoint inefficiencies, decrease waste production, and optimize processes and systems (Gargalo et al., 2021; Udugama et al., 2021).

DTs are built on a complex setup of coupled-up high-level technologies (hybrid modelling, IoT, Cloud computing, smart sensors, etc.). Smart technologies such as smart sensors are integral and critical parts of DTs. They are integrated to enable predictive maintenance and enhance performance. By combining data-driven techniques with conventional first principles-based models, hybrid modelling improves the predictive ability of digital twins by providing a more holistic way to predict and understand complex system behaviors. Thus, it leads to more accurate simulations and better management of resources and optimization due to having a more detailed and comprehensive understanding of the system and system dynamics (Boschert and Rosen, 2016; Tzachor et al., 2022; Sansana et al., 2021). DTs can monitor the real-time dynamic behavior of the physical running plant and experiment/simulate different conditions (‘what if’ scenarios) and resource allocation, thus optimizing resource consumption and allocation from supply to final production steps (Tzachor et al., 2022; Garske et al., 2024; Bauer et al., 2021). Of note is that hybrid modelling is especially useful in handling the multifaceted nature of sustainability, where there are multiple interacting elements and preexisting correlations (Bennett et al., 2005). For example, depicting the relationship between technical and economic factors and variables allows one to strategize to improve environmental impact while maintaining economic growth and prosperity and thus obtaining sustainable business models. Furthermore, in order to achieve the mentioned goals, DTs should enable decision-makers, policymakers, and scientists to evaluate environmental impact and human influence to make decisions that will indeed support sustainable development, as well as production and consumption, all safely within planetary boundaries (Garske et al., 2024; Li et al., 2023; Rockström et al., 2023).

By relying on digital transformation, hybrid modelling, and other enabling technologies, a symbiotic relationship is achieved between these concepts and DTs. Together, they drive optimization, resource efficiency, and sustainability - by leveraging these concepts and technologies, industries can positively contribute to sustainable development, where societal wellbeing aligns with environmental demands and economic growth (as pointed out by the 17 Sustainable Development Goals (Nations, 2024)).

Hybrid modelling integrates human expertise, in the form of domain-specific process knowledge, with data-driven information and machine learning techniques. In this work, to pinpoint essential concepts and critical insights regarding successful implementation, we have performed a pragmatic literature review of works exploring the use of hybrid modelling. It is noteworthy that hybrid modelling is paramount in the digital transformation of (bio)chemical industries (where intrinsically complex processes prevail) into Industry 4.0 and beyond. Some key takeaways are as follows.

• Holistic understanding and insights. The synergy obtained by applying hybrid modelling and thus integrating different sources of information can help with resource-intensive challenges (e.g., biopharma, enzyme production) and provide a more comprehensive understanding and overview of complex processes.

Furthermore, regarding the technical aspects of the successful development and implementation of hybrid models, the literature review has demonstrated that the main lessons are the effectiveness of hybrid models in providing robust predictions even with noise or sparse data, reducing the need for extensive datasets, the need to balance model accuracy with computational efficiency to ensure practicality in industrial applications, and the challenge of maintaining model interpretability, particularly in complex systems, to facilitate wider adoption and effective process control.

In summary, the transition towards digitalized operations can help the industry become resilient and attain remarkable levels of efficiency and sustainability. Thus, it is highly desirable and is on the agenda of most (bio) chemical industries. Since hybrid modelling plays a key role in this, it must be embraced and taken on as part of our toolset. Therefore, continuous efforts should be allocated to exploring different opportunities and implementation techniques and deep diving into developing and (when possible) sharing models for the digitalization of downstream and upstream processing steps at different scales.