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

2025-05-30

AI Summary

This work addresses the problem of predicting long-term statistical patterns and chaotic attractor evolution for the generalized Kuramoto–Sivashinsky (gKS) equation—a prototypical nonlinear partial differential equation exhibiting spatiotemporal chaos—under varying parameters such as dispersion relation and domain length. We propose a novel framework integrating echo state networks (ESNs) with transfer learning, enabling, for the first time, generalization of chaotic dynamics across distinct parameter regimes. Crucially, the model adapts to multiple unseen parameter configurations without retraining, accurately capturing structural changes in chaotic attractors. It preserves short-term trajectory accuracy while substantially improving robustness and cross-regime generalization for long-term statistical quantities—including power spectra, Lyapunov spectra, and invariant measures. This approach establishes a scalable, data-driven paradigm for modeling complex spatiotemporal chaotic systems.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

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. We introduce a novel methodology that integrates ESNs with transfer learning, aiming to enhance predictive performance across various parameter regimes of the gKS model. 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.

Problem

• Predict spatiotemporal chaos in Kuramoto-Sivashinsky equation
• Enhance prediction using echo state networks with transfer learning
• Capture changes in chaotic attractor from parameter variations

Innovation

• Echo state networks for chaotic systems prediction
• Transfer learning enhances ESN adaptability
• Captures attractor changes in varying parameters