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    Attention-enhanced reservoir computing as a multiple-dynamical-system approximator

    Felix Köster*, Kazutaka Kanno, and Atsushi Uchida†

    • Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan

    • *Contact author: felixk@mail.saitama-u.ac.jp
    • †Contact author: auchida@mail.saitama-u.ac.jp

    Phys. Rev. Applied 24, 054068 – Published 21 November, 2025

    DOI: https://doi.org/10.1103/7pv3-8792

    Abstract

    Reservoir computing has proven effective for tasks such as time-series prediction, particularly in the context of chaotic systems. However, conventional reservoir-computing frameworks often face challenges in achieving high prediction accuracy and adapting to diverse dynamical problems due to their reliance on fixed-weight structures. A concept of an attention-enhanced reservoir computing has been proposed, which integrates an attention mechanism into the output layer of the reservoir-computing model. This addition enables the system to prioritize distinct features dynamically, enhancing adaptability and prediction performance. In this study, we demonstrate the capability of the attention-enhanced reservoir computing to learn and predict multiple chaotic attractors simultaneously with a single set of weights, thus enabling transitions between attractors without explicit retraining. The main result shows that the attention-enhanced reservoir computing is able to distinguish different attractors just by learning from time-series samples. The method is validated using benchmark tasks, including the Lorenz system, the Rössler system, the Hénon map, the Duffing oscillator, and the Mackey-Glass delay-differential equation. Our results indicate that the attention-enhanced reservoir computing achieves superior prediction accuracy, valid prediction times, and improved representation of spectral and histogram characteristics compared to traditional reservoir-computing methods, establishing it as a robust tool for modeling complex dynamical systems.

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