A hybrid modeling methodology to combine prior knowledge and neural networks

We present a method to combine prior knowledge and artificial neural networks into a hybrid model. The hybrid exploits prior knowledge to guarantee predictions that are consistent with the process being modeled and to control extrapolation in the regions of input space that lack training data. Prior knowledge enters as two types of parametric models: (1) equality constraints upon the outputs, such as mass balances, and (2) a default model to control extrapolation. The nonparametric neural network compensates for uncertainty in describing process behavior. We demonstrate our approach by synthesizing a model of a fed-batch penicillin fermentation. Our results show that prior knowledge enhances the generalization capabilities of a pure neural network model. The hybrid provides more accurate predictions, which are consistent with the process constraints, and more reliable extrapolation.