Reconstruction of chaotic dynamics and robustness to noise with on-line EM algorithm

In this article, we discuss the reconstruction of chaotic dynamics by using a normalized Gaussian network (NGnet). Through using an on-line EM algorithm, the NGnet is trained to learn the vector field of the chaotic dynamics. We also investigate the robustness of our approach to two kinds of noise processes: system noise and observation noise. We have found that a trained NGnet is able to reproduce a chaotic attractor, even under these two kinds of noise. The trained NGnet also exhibits good prediction performance. When part of the dynamical variables is observed, a delay coordinate embedding is used; namely, the NGnet is trained to learn the vector field in the delay coordinate space. It is shown that the chaotic dynamics can be learned with this method even under two kinds of noise.