Forecasting Nonlinear Systems with Neural Networks via Anticipated Synchronization

Abstract

Predictability of chaotic nonlinear systems is limited by the exponential propagation of errors characteristic of chaotic behavior. In this paper we analyze a new nonlinear prediction scheme considering a chain of identical neural networks synchronized to the original system using an anticipated setting. The neural models are fitted to a time series obtained from an embedding of a scalar observable of the original system (e.g., a single variable). The spatiotemporal dynamics of the resulting chain model are analyzed and the maximum prediction horizons attainable with this scheme are estimated. Although it is possible in theory to obtain arbitrary long forecast horizons with this methodology, we show that even tiny errors (e.g., the errors introduced in the modeling phase) limit severely the attainable prediction horizons in practical applications.