Attractor reconstruction by machine learning

Zhixin Lu; Brian R Hunt; Edward Ott

doi:10.1063/1.5039508

Attractor reconstruction by machine learning

Chaos. 2018 Jun;28(6):061104. doi: 10.1063/1.5039508.

Authors

Zhixin Lu¹, Brian R Hunt², Edward Ott³

Affiliations

¹ Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
² Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
³ Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.

PMID: 29960382
DOI: 10.1063/1.5039508

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.