Combined Mechanistic and Empirical Modelling

We consider a hybrid modelling approach based on the combination of prior knowledge, in the form of mechanistic models, with tools for the extraction of knowledge from operating data: the first component captures first-principles system behavior features, while the second one accounts for the differences found between mechanistic predictions and real data. The empirical modelling methods tested include backpropagation Artificial Neural Networks (ANN), Multivariate Adaptive Regressive Splines (MARS) and Regression Analysis (RA). In the proposed hybrid structure, mechanistic predictions provide additional inputs for the empirical module. To evaluate the performance of the various combinations of modules and hybrid approaches, we consider two simulated case studies (involving a CSTR with a reversible reaction and a fed-batch penicillin fermentation process). In all of the above, our hybrid structure based on a mechanistic module together with an empirical component has outperformed other approaches, and the mechanistic model/MARS combination resulted in lowest overall prediction errors.