A general deep hybrid model for bioreactor systems: combining First Principles with deep neural networks

Numerous studies have reported the use of hybrid semiparametric systems that combine shallow neural networks with First Principles for bioprocess modeling. Here we revisit the general bioreactor hybrid model and introduce some deep learning techniques. Multi-layer networks with varying depths were combined with First Principles equations in the form of deep hybrid models. Deep learning techniques, namely the adaptive moment estimation method (ADAM), stochastic regularization and depth-dependent weights initialization were evaluated in a hybrid modeling context. Modified sensitivity equations are proposed for the computation of gradients in order to reduce CPU time for the training of deep hybrid models. The methods are illustrated with applications to a synthetic dataset and a pilot 50 L MUT+ Pichia pastoris process expressing a single chain antibody fragment. All in all, the results point to a systematic generalization improvement of deep hybrid models over its shallow counterpart. Moreover, the CPU cost to train the deep hybrid models is shown to be lower than for the shallow counterpart. In the pilot 50L MUT+ Pichia pastoris data set, the prediction accuracy was increased by 18.4% and the CPU decreased by 43.4%.