Surrogate Modeling of Microbial PHA-Biopolymer Synthesis

Sophisticated control and optimization of biotechnological processes, such as production of polyhydroxyalkaonate (PHA) biopolymers, require mathematical models, which allow accurate representation of the process dynamics and also exhibit a moderate degree complexity. One possible solution is found in surrogate modeling. Here, simulations of (complex) first-principles process models are used to design suitable model formulations of moderate complexity that can subsequently be used for model-based process control and optimization. In this contribution, dynamic mode decomposition with control (DMDc), including a time-delay embedding is applied to derive surrogate models for a fed-batch and a continuous production of two specific PHAs, namely, poly(3-hydroxybutyrate) (PHB) and bioco-polymer poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV), using simulation data of a recently presented highly nonlinear first-principles process model. The obtained surrogates are reduced order discrete-time linear models, which allow for efficient application of established linear control and optimization techniques. Predictive capabilities of the surrogates are evaluated for in silico validation experiments. It is shown that the nonlinear process dynamics can be approximated accurately by the surrogates, and the latter are thereby a valuable tool for subsequent process optimization. Studies for different orders of time-delay embedding indicate that more detailed embeddings yield improved accuracy. This effect becomes less pronounced when further increasing the embeddings complexity. Furthermore, it is also shown for a repeated fed-batch setup that the extrapolative capabilities of the fed-batch surrogate for related but different process setups are limited and can only approximate the nonlinear process behavior qualitatively.