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

Jason A Platt; Stephen G Penny; Timothy A Smith; Tse-Chun Chen; Henry D I Abarbanel

doi:10.1063/5.0156999

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

Chaos. 2023 Oct 1;33(10):103107. doi: 10.1063/5.0156999.

Authors

Jason A Platt¹, Stephen G Penny^{2

3}, Timothy A Smith^{3

4}, Tse-Chun Chen⁵, Henry D I Abarbanel^{1

6}

Affiliations

¹ Department of Physics, University of California San Diego, San Diego, California 92093, USA.
² Sofar Ocean, 28 Pier Annex, San Francisco, California 94105, USA.
³ Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, Colorado 80309, USA.
⁴ Physical Sciences Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado 80305, USA.
⁵ Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, Washington 99354, USA.
⁶ Marine Physical Laboratory, Scripps Institution of Oceanography, 9500 Gilman Drive, La Jolla, California 92093, USA.

PMID: 37788385
DOI: 10.1063/5.0156999

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.