Neural network reconstruction and prediction of chaotic dynamics

The work is devoted to the use of multilayer nonlinear perceptrons, trained with backpropagation, for reconstructing five known chaotic dynamics from their temporal series. In the case of finite-dimensional dynamics the authors tested the behavior of different structures and compared them with the results that can be obtained by using a quite different approach, i.e., functional reconstruction. The sigmoidal characteristic of neurons seems to lead to a better performance when dealing with a nonpolynomial dynamics. In the case of an infinite-dimensional dynamics the dependence of the prediction error on the size of the net and the delay parameter of the dynamics were investigated experimentally. Some hints for choosing network architecture and learning strategy are presented together with some suggestions for furthering such an investigation