Indirect training of grey-box models: application to a bioprocess

Grey-box neural models mix differential equations, which act as white boxes, and neural networks, used as black boxes. The purpose of the present work is to show the training of a grey-box model by means of indirect backpropagation and Levenberg-Marquardt in Matlab®, extending the black box neural model in order to fit the discretized equations of the phenomenological model. The obtained grey-box model is tested as an estimator of a state variable of a biotechnological batch fermentation process on solid substrate, with good results. © Springer-Verlag Berlin Heidelberg 2007.