Symmetry enhanced prediction of spatio-temporal chaotic system with reservoir computing

Xiaoqi Lei, Zixiang Yan, Hui Zhao, Jian Gao, Yueheng Lan and Jinghua Xiao

Chaos, Solitons & Fractals, 2026, vol. 202, issue P2

Abstract: The prediction of spatio-temporal chaotic systems has considerable potential for applications across diverse domains, ranging from climate systems to financial markets. With the advancement of machine learning techniques, model-free prediction based on data from such systems has attracted substantial attention. However, the complex patterns and high-dimensional dynamics inherent to spatio-temporal chaotic systems pose significant challenges for conventional machine learning methods. To address this challenge, we propose the multiplexing local reservoir computing, a novel approach that integrates the inherent symmetry and localization of spatio-temporal systems with reservoir computing. Specifically, the new method uses spatial translation symmetry to combine the data among different locations and train a single reservoir to predict the evolution based on local information. After training, such multiplexing local reservoir can be used to predict the evolution of all locations separately. Because of the parameter-aware approach, the new method can be generalized to heterogeneous systems with local parameters. We demonstrate the efficacy of the multiplexing local reservoir computing using the classic spatio-temporal chaotic system, coupled map lattice, encompassing cases with homogeneous or heterogeneous, and known or unknown local parameters. Our new method greatly reduces the amount of training data required and improves prediction performance. Other spatio-temporal chaotic systems, such as Kuramoto-Sivashinsky system and Lorenz-96 model, are also used to validate the method. The multiplexing local reservoir computing framework proposed in this work not only offers an efficient tool but also paves the way for integrating physical information of dynamical systems with machine learning techniques.

Keywords: Reservoir computing; Spatio-temporal chaotic system; Coupled map lattices (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925016479

DOI: 10.1016/j.chaos.2025.117634

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