(424f) Functional-Hybrid Models for Interpretable Modeling of Bioprocesses

The plethora of mathematical models in science and engineering available can be broadly classified into two paradigms: (i) data-driven, statistical or (Machine Learning (ML)) models, and (ii) first principle based (mechanistic, white box) models. Both approaches have their own advantages and disadvantages and a choice is made based on the prior understanding about the system and the availability of data. Hybrid models that are capable of integrating engineering know-how (first-principle models) with data (machine learning), have become a pragmatic solution to modeling in different areas of chemical engineering and biotechnology. Most of the hybrid modeling work pose basic mass or energy balances and some preliminary dependencies and approximate unknown relationships with data-driven models.

However, the data-driven part of these hybrid models is largely dependent on conventional machine learning methods such as artificial neural networks, support vector machines, Gaussian processes, etc., thus making it difficult for process engineers to interpret the patterns learned by these models. On the other hand, there are common functional forms specific to each domain that is easily recognized by experts. In general, the scope of modelling is to arrive to a mathematical formulation that explains the observations of a system sufficiently well, is as simple as possible and is interpretable by the domain-experts. Thus, in order to develop a robust but simultaneously interpretable hybrid model, it is essential to incorporate these domain expert considerations in a strategic manner while still ensuring flexibility.

In this direction, in this work, we presented a novel hybrid modeling framework, called Functional-Hybrid models. This framework uses domain-specific ranked functional forms using symbolic regression to build dynamic models that allow for interpretability by the domain experts.

The thus developed framework is first tested for its ability to represent observation accurately and the interpretability offered by the final models. Secondly, the developed Functional-Hybrid model is compared against a conventional architecture with a hybrid model based on an artificial neural network (Hybrid-ANN) for a microbial fermentation process. The models are compared based on their accuracy in interpolation and extrapolation where we could demonstrate that the Functional-Hybrid model has at least 2-times lower errors compared to Hybrid-ANN. Further, the experimental cost required to develop these models are evaluated in terms of the number of experiments required to develop a robust model for either case with Functional-Hybrid models requiring only 20 experiments while the Hybrid-ANN needed at least 40 experiments. The additional structure enforced by the domain-specific functional transformations in the Functional-Hybrid model provides it the robustness in predictions specifically extrapolation and reduces the requirement of experiments to train such models.

To demonstrate the concept, the case studies presented in this work are based on simulations. However, the transfer of this approach to real use cases is the foreseen next steps in this direction. Additionally, the current framework is not optimized to have a high computational speed. The next steps involve improving the numerical efficiency of the part of the framework to increase the computation efficiency of the proposed framework.