NEURAL LEARNING OF CHAOTIC SYSTEM BEHAVIOR

We introduce recurrent networks that are able to learn chaotic maps, a nd investigate whether the neural models also capture the dynamical in variants (Correlation Dimension, largest Lyapunov exponent) of chaotic time series. We show that the dynamical invariants can be learned alr eady by feedforward neural networks, but that recurrent learning impro ves the dynamical modeling of the time series. We discover a novel typ e of overtraining which corresponds to the forgetting of the largest L yapunov exponent during learning and call this phenomenon dynamical ov ertraining. Furthermore, we introduce a penalty term that involves a d ynamical invariant of the network and avoids dynamical overtraining. A s examples we use the Henon map, the logistic map and a real world cha otic series that corresponds to the concentration of one of the chemic als as a function of time in experiments on the Belousov-Zhabotinskii reaction in a well-stirred flow reactor.