Neural learning of chaotic dynamics

摘要

In recent years, considerable progress has been made in modeling chaotic time series with neural networks. Most of the work concentrates on the development of architectures and learning paradigms that minimize the prediction error. A more detailed analysis of modeling chaotic systems involves the calculation of the dynamical invariants which characterize a chaotic attractor. The features of the chaotic attractor are captured during learning only if the neural network learns the dynamical invariants. The two most important of these are the largest Lyapunov exponent which contains information on how far in the future predictions are possible, and the Correlation or Fractal Dimension which indicates how complex the dynamical system is. An additional useful quantity is the power spectrum of a time series which characterizes the dynamics of the system as well, and this in a more thorough form than the prediction error does.