Model-free prediction of chaotic dynamics with parameter-aware reservoir computing

Abstract Model-free, data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science. Stimulated by the recent progress in machine learning, considerable attention has been given to the inference of chaos by the technique of reservoir computing (RC). In particular, by incorporating a parameter-control channel into the standard RC, it is demonstrated that the machine is able to not only replicate the dynamics of the training states, but also infer new dynamics not included in the training set. The new machine-learning scheme, termed parameter-aware RC, opens up new avenues for data-based analysis of chaotic systems, and holds promise for predicting and controlling many real-world complex systems. Here, using typical chaotic systems as examples, we give a comprehensive introduction to this powerful machine-learning technique, including the algorithm, the implementation, the performance, and the open questions calling for further studies.