Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks

Jason A. Platt, Stephen G. Penny, Timothy A. Smith, Tse-Chun Chen, Henry D. I. Abarbanel
4/24/2023
cs.LGmath.DSphysics.geo-ph

No official code found. Best implementation: japlatt/BasicReservoirComputing (33 stars, MIT, last commit 2022-04-27).

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 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 the recurrent neural network architecture of reservoir computing. Results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model, both typical test cases for numerical weather prediction.

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Code Implementations(1)

japlatt/BasicReservoirComputingCommunity100%
MIT

Implementation of a reservoir computer with functions to optimize the parameters and calculate the Lyapunov exponents

338JuliaFeb 9, 20224 years agoMIT

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Cite this paper

@article{platt2023constraining,
  title  = {Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks},
  author = {Jason A. Platt and Stephen G. Penny and Timothy A. Smith and Tse-Chun Chen and Henry D. I. Abarbanel},
  year   = {2023},
  eprint = {2304.12865},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2304.12865v1}
}

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