Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers-Reference-Cited by-同舟云学术

Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

Published:2023-10-01 Issue:10 Volume:33 Page:
ISSN:1054-1500
Container-title:Chaos: An Interdisciplinary Journal of Nonlinear Science
language:en
Short-container-title:

Author:

Platt Jason A.¹^ORCID,Penny Stephen G.²³^ORCID,Smith Timothy A.³⁴^ORCID,Chen Tse-Chun⁵^ORCID,Abarbanel Henry D. I.¹⁶^ORCID

Affiliation:

1. Department of Physics, University of California San Diego 1 , San Diego, California 92093, USA

2. Sofar Ocean 2 , 28 Pier Annex, San Francisco, California 94105, USA

3. Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder 3 , Boulder, Colorado 80309, USA

4. Physical Sciences Laboratory, National Oceanic and Atmospheric Administration 4 , Boulder, Colorado 80305, USA

5. Pacific Northwest National Laboratory 5 , 902 Battelle Blvd, Richland, Washington 99354, USA

6. Marine Physical Laboratory, Scripps Institution of Oceanography 6 , 9500 Gilman Drive, La Jolla, California 92093, USA

Abstract

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants—such as the Lyapunov exponent spectrum and the fractal dimension—in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.

Funder

Office of Naval Research

National Oceanic and Atmospheric Administration

Cooperative Institute for Research in Environmental Sciences

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0156999/18150293/103107_1_5.0156999.pdf

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