Attractor Reconstruction by Machine Learning

TL;DR

This paper develops a theoretical framework for reservoir computing, a machine learning method, demonstrating its effectiveness in short-term prediction and attractor reconstruction of chaotic systems, supported by numerical experiments.

Contribution

It provides the first theoretical conditions under which reservoir computing can accurately model chaotic dynamical systems from time series data.

Findings

Reservoir computing can achieve skillful short-term forecasts.

Theoretical conditions for effective attractor reconstruction are established.

Numerical experiments validate the theoretical predictions.

Abstract

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes conditions under which reservoir computing can create an empirical model capable of skillful short-term forecasts and accurate long-term ergodic behavior. We illustrate this theory through numerical experiments. We also argue that the theory applies to certain other machine learning methods for time series prediction.