Learning chaotic dynamics by neural networks

We show that neural networks can accurately learn the dynamical laws of chaotic time series from a limited number of iterates. Moreover, for short-term predictions they clearly outperform conventional methods, like, for instance, linear autoregressive models and a nonlinear simplex-like algorithm. We reconstruct the dynamics of computer-generated data corresponding to the logistic equation-which is known to have negligible autocorrelation-and the Lorenz map-which has significant autocorrelation-. Unlike previous claims in the literature, in both cases properly trained neural networks show better predictive skill than the autoregressive and simplex-like models. Finally, we discuss briefly applications of neural networks in the analysis of real-world time series.