Model-free Machine Learning Analysis of Chaotic Dynamics Including that of Large Spatiotemporally Chaotic Systems

We consider the common situation in which a finite length time-series data produced by a chaotic dynamical system is available, and it is desired to infer dynamical information solely from this data (i.e., in the absence of knowledge of the data-generating system itself). Examples of the types of infered information that it might be desired to are the future evolution of the system (i.e., the task of prediction), the Lyapunov exponents of the system generating the data, and the inference of unmeasured state variables from future partial measurements. Using the machine learning technique known as Reservoir Computing we show how these tasks can be accomplished. In particular, use as illustrative examples low dimensional chaotic systems, as well as high dimensional extensively chaotic spatiotemporal systems. Our general conclusion is that machine learning is exceptionally good performing tasks of this type, and, in some cases can accomplish these tasks in situations for which successful previous methods are not available. [Collaborators: Jaideep Pathak, Zhixin Lu, Brian Hunt, Michelle Girvan.]