Assessing and improving the replication of chaotic attractors by means of reservoir computing

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, the so-called "reservoir computing" method turned out to be a very promising approach especially for the reproduction of the long-term properties of the system [1]. Yet, a thorough statistical analysis of the forecast results is missing. So far the standard approach is to use purely random Erdos-Renyi networks for the reservoir in the model. It is obvious that there is a variety of conceivable network topologies that may have an influence on the results. Using the Lorenz System we statistically analyze the quality of predicition for different parametrizations - both the exact short term prediction as well as the reproduction of the long-term properties of the system as estimated by the correlation dimension and largest Lyapunov exponent. We find that both short and longterm predictions vary significantly. Thus special care must be taken in selecting the good predictions. We investigate the benefit of using different network topologies such as Small World or Scale Free networks and show which effect they have on the prediction quality. Our results suggest that the overall performance is best for small world networks. [1] J. Pathak et al., Chaos, 27, 121102 (2017)