Reservoir Computing Meeting Kolmogorov-Arnold Networks: Prediction of High-Dimensional Chaotic Systems

Abstract

The prediction of high-dimensional chaotic time series is a widely concerned and highly challenging task. We propose a novel method, Reservoir Computing with Kolmogorov-Arnold networks, that combines reservoir computing and Kolmogorov-Arnold networks to address this difficult issue. The proposed method involves replacing the linear output layer of traditional reservoir computing with Kolmogorov-Arnold networks, and employs a training scheme that incorporates the teacher-forcing mode and the free-running mode during the training process, respectively. We utilize the Lorenz-96 system and the Kuramoto-Sivashinsky equation as two examples of high-dimensional chaotic systems to illustrate the feasibility of our method. The results of comparative experiments demonstrate that our method exhibits superior prediction capabilities and maintains robustness in the presence of noise perturbation and hyperparameter variations.

Keywords: Reservoir Computing, Kolmogorov-Arnold Networks, High-Dimensional Chaotic Time Series