Long-term prediction of chaotic systems with machine learning

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has been about half dozen Lyapunov time. Is it possible to significantly extend the prediction time beyond what has been achieved so far? We articulate a scheme incorporating time-dependent but sparse data inputs into reservoir computing and demonstrate that such rare "updates"of the actual state practically enable an arbitrarily long prediction horizon for a variety of chaotic systems. A physical understanding based on the theory of temporal synchronization is developed.