Reconstruction of chaotic dynamics using a noise-robust embedding method

In this article, we discuss the reconstruction of chaotic dynamics in a partial observation situation. As a function approximator, we employ a normalized Gaussian network (NGnet), which is trained by an on-line EM algorithm. In order to deal with the partial observation, we propose a new embedding method based on smoothing filters, which is called integral embedding. The NGnet is trained to learn the dynamical system in the integral coordinate space. Experimental results show that the trained NGnet is able to reproduce a chaotic attractor that well approximates the complexity and instability of the original chaotic attractor, even when the data involve large noise. In comparison with our previous method using delay coordinate embedding, this new method is more robust to noise and faster in learning.