Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach

Jaideep Pathak, Brian Hunt, Michelle Girvan, Zhixin Lu, and Edward Ott

Phys. Rev. Lett. 120, 024102 – Published 12 January 2018

Abstract

We demonstrate the effectiveness of using machine learning for model-free prediction of spatiotemporally chaotic systems of arbitrarily large spatial extent and attractor dimension purely from observations of the system’s past evolution. We present a parallel scheme with an example implementation based on the reservoir computing paradigm and demonstrate the scalability of our scheme using the Kuramoto-Sivashinsky equation as an example of a spatiotemporally chaotic system.

Received 24 July 2017
Revised 23 November 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.024102

Physics Subject Headings (PhySH)

Chaos Dynamics of networks Spatiotemporal chaos

Chaotic systems Dynamical systems High dimensional systems

Time series analysis

Nonlinear Dynamics

Authors & Affiliations

Jaideep Pathak^1,2,*, Brian Hunt^3,4, Michelle Girvan^1,3,2, Zhixin Lu^1,3, and Edward Ott^1,2,5

¹Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
²Department of Physics, University of Maryland, College Park, Maryland 20742, USA
³Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
⁴Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
⁵Department of Electrical and Computer Engineering, University of Maryland, Maryland 20742, USA