Quantum mechanics

Algorithm

Chaotic

Biology

Applied mathematics

Time series

Computer science

Reservoir computing

Paleontology

Physics

Mathematics

Attractor

Mathematical analysis

Artificial intelligence

Series (stratigraphy)

Dynamical systems theory

Term (time)

Artificial neural network

Ergodic theory

Recurrent neural network

Machine learning

Chaos An Interdisciplinary Journal of Nonlinear Science

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.

Attractor reconstruction by machine learning