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

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

doi:10.1063/5.0156999

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

2023
By Platt, Jason A. ; Penny, Stephen G. ; Smith, Timothy A. ; ...
Source: Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(10)

[PDF-1.63 MB]

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Journal Title:

Chaos: An Interdisciplinary Journal of Nonlinear Science
Personal Author:

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

Platt, Jason A. ; Penny, Stephen G. ; Smith, Timothy A. ; Chen, Tse-Chun ; Abarbanel, Henry D. I. Less -
NOAA Program & Office:

OAR (Oceanic and Atmospheric Research) ; CIRES (Cooperative Institute for Research in Environmental Sciences) ; PSL (Physical Sciences Laboratory)

OAR (Oceanic and Atmospheric Research) ; CIRES (Cooperative Institute for Research in Environmental Sciences) ; PSL (Physical Sciences Laboratory) Less -
Description:

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.
Keywords:

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Applied Mathematics General Physics And Astronomy Mathematical Physics Statistical And Nonlinear Physics
Source:

Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(10)
DOI:

https://doi.org/10.1063/5.0156999
ISSN:

1054-1500;1089-7682;
Format:

PDF
Publisher:

AIP Publishing
Document Type:

Journal Article
Funding:

Grant no. NA17OAR4320101 ; Grant no. NA20OAR4600277

Grant no. NA17OAR4320101 ; Grant no. NA20OAR4600277 Less -
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urn:sha256:84572a03ef172b0bcb2a32e924b6f74336daad3c5f4a7b7313a1726cd603ce6b
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https://staging-noaa.cdc.gov/view/noaa/57914/noaa_57914_DS1.pdf
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Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

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