Using artificial neural networks to forecast chaotic time series

Two-layer feedforward neural network was used in this work to forecast chaotic time series with very promising results, especially for the Lorenz system, as in comparison to others that had been previously published elsewhere. It was observed that the architecture m:2m: m:1, where in is the embedding dimension of the attractor of the dynamical system in consideration, is a very good initial guess for the process of finding the ideal architecture for the neural network, which is usually hard to achieve. The results we obtained with this particular type to series, and also with some others like Henon and Logistic maps, clearly indicate that there is an interplay between the architecture of a multilayer network and the embedding dimension nt of the time series used. From the very good forecasting results we obtained, it can be concluded that neural networks can be considered to be an important tool for making predictions of the time evolution of nonlinear systems. (C) 2000 Elsevier Science B.V. All rights reserved.