Nonlinear Balanced Model Residualization via Neural Networks

This paper introduces a new model reduction approach for nonlinear systems, which retains most of the input-output properties of the original system. In a first step a nonlinear model reduction using balancing based upon empirical gramians is implemented. Then in a second step, the resulting residualized system is further reduced using neural networks in order to make it faster to compute. Special attention is given to the choice of training sets for the neural network. Three different training sets are examined and the effect they have on the accuracy of the resulting reduced model is compared. This method is demonstrated through examples. The final reduced system is easy to compute and highly accurate. The presented method requires no assumptions about the controllability/observability of the original model.