Long-term prediction of chaotic systems with recurrent neural networks

TL;DR

This paper introduces a novel reservoir computing approach with sparse, time-dependent data inputs that significantly extends the prediction horizon for chaotic systems, surpassing previous limits.

Contribution

It proposes a new scheme incorporating sparse data updates into reservoir computing, enabling arbitrarily long predictions of chaotic systems.

Findings

Extended prediction horizon beyond Lyapunov time

Sparse data updates improve long-term prediction accuracy

Physical understanding based on temporal synchronization

Abstract

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.