A New Generic Mass Balance Model with Multi-Layer Perceptron-Based Kinetics and Stoichiometry

This paper proposes a new generic mass balance model that allows simulating biological cultures in bioreactors at a macroscopic scale. A multi-layer perceptron (MLP) describes the kinetic and stoichiometric parts of the model with one input layer (made of the concentrations of the different components, as well as their inverse TReLU – Thresholded Rectified Linear Unit – transforms), one hidden layer (each neuron output corresponding to one specific reaction rate and being activated by a reciprocal function 1 / x ) and one output layer (each neuron output being the sum of all the reaction contributions of a specific component to its mass balance). The parameters to be identified are split into two subsets: one for the kinetic parameters (weights on the links between input layer and hidden layer) and one for the stoichiometric parameters (weights on the links between hidden layer and output layer). This MLP structure exhibits several advantages, among which its versatility, the biological interpretation of the parameters, and an easy and efficient first estimation of the kinetic and stoichiometric parameters based on measurements of the component concentrations and estimations of their time derivatives. The first parameter estimation can subsequently be used for model reduction and as initial guess for a final nonlinear parameter estimation of the set of ODEs describing the mass balances. The performances of the new generic model are illustrated with a simulated case study.