(106b) Hybrid Modeling of Bioprocesses Based on a Kinetic Canonical Formalism

In recent years, mathematical modeling techniques and simulations have gained increasing attention in the biopharmaceutical industry [1]. These tools are helpful in a range of areas, including guiding experiments more effectively, supporting process monitoring and control tasks, stabilizing product quality, increasing consumer safety, and easing specific decision-making tasks for subject matter experts.
Modeling biotechnological processes is particularly challenging due to its inherent complexity, making it very difficult to precisely describe the underlying metabolic mechanisms dictating the microorganisms’ behavior [2]–[5]. However, modeling these pathways is key for producing therapeutic compounds so that the associated processes can be optimized effectively [1]. Ideally, modelers have addressed this problem by combining well-defined kinetic expressions with available data (semi-empirical or deterministic) to support the efficient and cost-effective development of new therapeutic drugs [6]. However, choosing a well-suitable kinetic expression and calibrating it with experimental points is particularly challenging. Such methods involve the solution of nonconvex dynamic optimization problems that can lead to high computational costs and several suboptimal solutions.
As an alternative to mechanistic models, data-driven strategies allow studying the system’s behavior without relying on detailed expert knowledge [7], [8]. An advantage of such process models is that they only require data and can be set up without any deep understanding of the underlying system. However, they are hard to interpret and may return values that are not consistent with the physical laws governing the underlying system due to the few mechanistic constraints imposed during training. As a bridge between deterministic and data-driven methods, hybrid modeling has recently gained popularity to exploit their complementary advantages. In essence, hybrid models combine a mechanistic backbone with a surrogate component, with their specific structure depending on the problem at hand. While this modeling approach is well known, how to optimally define hybrid models for bioprocesses remains challenging, including the choice of mechanistic and black-box components and their optimal level of hybridization.
This work proposes a hybrid modeling approach based on an S-system canonical formalism that automatically builds kinetic models of bioprocesses from experimental observations. The proposed methodology determines the model structure and parameters during the model-building procedure. Notably, our hybrid approach combines a first-principles backbone based on mass balances with a canonical kinetic S-system formalism, whose structure and model parameters are automatically identified by solving a mixed-integer nonlinear program (MINLP). Our approach significantly tightens the search space by applying “rational” constraints to the structure of the model. The model training is performed following a two-stage procedure that simplifies the calculations by avoiding the iterative integration of differential equations.
Numerical examples show that our method performs similarly to hybrid models based on artificial neural networks, with the advantage of obtaining a compact, analytical canonical expression. Such a hybrid model based on a canonical formalism allows modelers to extract information about the processes and generate further insight into their behavior. In this context, the proposed MINLP approach helps screen and adjust the complexity of the hybrid model. Hence, our approach could help find a suitable process model while simultaneously allowing practitioners to analyze the underlying formulation more quickly and use it in subsequent optimization studies.

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