Improvements in the predictive capability of neural networks

Neural networks can be used to develop effective models of nonlinear systems. Their main advantage being that they can model the vast majority of nonlinear systems to any arbitrary degree of accuracy. The ability of a neural network to predict the behavior of a nonlinear system accurately ought to be improved if there was some mechanism that allows the incorporation of first-principles model information into their training. This study proposes to use information obtained from a first-principle model to impart a sense of “direction” to the neural network model estimate. This is accomplished by modifying the objective function so as to include an additional term that is the difference between the time derivative of the outputs, as predicted by the neural network, and that of the outputs of the first-principles model during the training phase. The performance of a feedforward neural network model that uses this modified objective function is demonstrated on a chaotic process and compared to the conventional feedforward network trained on the usual objective function.