Hybrid modeling of glycerol fermentation process based on deep neural networks and mechanistic models

Microbial fermentation is essentially a complex cellular metabolic process that involves both intracellular and extracellular metabolic environment. Hybrid modeling is an effective and popular method for modeling microbial fermentation process by combining data-driven models with mechanistic models. This paper focuses on neural network-based hybrid modeling of the bioconversion process of glycerol to 1,3-propanediol by Klebsiella pneumoniae in continuous fermentation. Several suitable deep neural networks are constructed to characterize intracellular metabolic dynamics and then embedded into the extracellular mechanistic model to develop two different hybrid models under serial and parallel schemes. With the minimization of the loss function as the optimization objective, two large-scale parameter optimization problems are given to determine the model parameters of neural networks. To solve these optimization problems, a parallel optimization algorithm is designed based on an improved fruit fly optimization algorithm (FOA) and parfor parallel computing. Numerical results demonstrate that the proposed hybrid models can not only significantly improve the accuracy of metabolite concentration fitting (with the substrate reaching [Formula: see text]), but also enable a more precise prediction of steady-state concentrations in continuous glycerol fermentation. Furthermore, numerical comparisons indicate that the improved FOA can achieve an improvement of [Formula: see text] in solution accuracy and an increase of [Formula: see text] in computational efficiency, compared to the basic FOA. This work can be a reference for modeling and numerical solutions of complicated practical optimization problems.