Bioprocess hybrid parametric/nonparametric modelling based on the concept of mixture of experts

This paper presents a novel method for bioprocess hybrid parametric/nonparametric modelling based on mixture of experts (ME) and the expectation maximisation (EM) algorithm. The bioreactor system is described by material balance equations whereas the cell population subsystem is described by an adjustable mixture of parametric/nonparametric sub-models inspired in the ME architecture. This idea was motivated by the fact that cellular metabolism has an inherent “modular” structure, organised in metabolic pathways, with complex interactions. This study was supported by simulations using models of different levels of complexity. The proposed method was compared with the conventional hybrid technique employing the multi-layer perceptron (MLP) and the radial basis function (RBF) networks. As main conclusions it can be stated that MEs trained with the EM algorithm are able to systematically detect metabolic shifts with the individual experts developing expertise in describing the individual pathways. The hybrid ME model with thin-plate spline RBF network as experts outperforms both the hybrid MLP model and the hybrid RBF model in its ability to describe metabolic switches.