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of overparametrization in non-linear system identification and neural networks

The effects of overparametrization in non-linear system identification and neural networks are often presented as overfitting to a particular data set. An overparametrized model tends to interpolate the data set and can fail to capture the underlying dynamics represented by the data. Past studies have usually concentrated on overparametrisation in the number of model terms or the number of hidden layer nodes. In the present study, the effects of several forms of overparametrization on the model dynamics are compared using qualitative validation methods. The dynamic properties of the identified model or the trained network are graphically displayed and compared with those of the real system. It is shown that overparametrization in the number of time lags or input nodes has the worst effect on the dynamic properties of the resulting model.