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Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning

arXiv 2505.24099 ↗First posted 30 May 2025math.DS cs.AI cs.LGcited by 0

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Abstract (arXiv)

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibits spatiotemporal chaos. Our research focuses on predicting changes in long-term statistical patterns of the gKS model that result from varying the dispersion relation or the length of the spatial domain. We use transfer learning to adapt ESNs to different parameter settings and successfully capture changes in the underlying chaotic attractor. Previous work has shown that transfer learning can be used effectively with ESNs for single-orbit prediction. The novelty of our paper lies in our use of this pairing to predict the long-term statistical properties of spatiotemporally chaotic PDEs. We also show that transfer learning nontrivially improves the length of time that predictions of individual gKS trajectories remain accurate.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 14 of its 63 references that are in the map. First posted on arXiv 30 May 2025.

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References · 14

  1. 2019Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamicscited by 132
  2. 2021Scikit-dimension: a Python package for intrinsic dimension estimationcited by 68
  3. 2020Machine learning prediction of critical transition and system collapsecited by 54
  4. 2022Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systemscited by 33
  5. 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamicscited by 27
  6. 2023A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learningcited by 22
  7. 2018Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptographycited by 16
  8. 2020Physics-Informed Echo State Networkscited by 16
  9. 2020Reservoir computing model of two-dimensional turbulent convectioncited by 15
  10. 2021Reservoir Computing as a Tool for Climate Predictability Studiescited by 13
  11. 2019Separation of Chaotic Signals by Reservoir Computingcited by 12
  12. 2020Transfer learning for nonlinear dynamics and its application to fluid turbulencecited by 9
2 more
  1. 2021Echo State Network for two-dimensional turbulent moist Rayleigh-B'enard convectioncited by 4
  2. 2021Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learningcited by 3

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