Nonlinear Models for Characterization and Prediction of Noisy Chaotic Times Series

We describe a nonlinear modelling algorithm capable of accurately capturing dynamics from short noisy time series. This method utilises an information theoretic model selection criteria and a variant of the artificial neural network (ANN) modelling scheme. The ANN consists of a single hidden layer and a monotonic nonlinear output function. The hidden layer is composed of a relatively small number of carefully selected neurons, the number of neurons in the optimal ANN is determined by the minimum description length (MDL) model selection criteria. The MDL best model is the model that captures only the essential deterministic features of the data.

We apply this modelling algorithm to several computational and experimental systems including chaotic differential equations, the annual sunspot count, and a chaotic laser. In each case we show that the optimal model captures the chaotic dynamics of the underlying system but does not t deterministic structure to system noise.