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

arXiv: https://arxiv.org/abs/2505.24099 · HTML: https://mlsanity.com/paper/2505.24099/

## Key facts

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

## Builds on (most cited first, 14 of 14)

- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2207.00521/) (2022)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning](https://mlsanity.com/paper/2307.15092/) (2023)
- [Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography](https://mlsanity.com/paper/1802.02844/) (2018)
- [Physics-Informed Echo State Networks](https://mlsanity.com/paper/2011.02280/) (2020)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)
- [Reservoir Computing as a Tool for Climate Predictability Studies](https://mlsanity.com/paper/2103.06206/) (2021)
- [Separation of Chaotic Signals by Reservoir Computing](https://mlsanity.com/paper/1910.10080/) (2019)
- [Transfer learning for nonlinear dynamics and its application to fluid turbulence](https://mlsanity.com/paper/2009.01407/) (2020)
- [Echo State Network for two-dimensional turbulent moist Rayleigh-B'enard convection](https://mlsanity.com/paper/2101.11325/) (2021)
- [Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning](https://mlsanity.com/paper/2112.09182/) (2021)

## 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.