Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction

Xin Li, Qunxi Zhu (), Chengli Zhao (), Xiaojun Duan, Bolin Zhao, Xue Zhang, Huanfei Ma, Jie Sun and Wei Lin ()
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Xin Li: Center for Applied Mathematics (NUDT)
Qunxi Zhu: Fudan University
Chengli Zhao: Center for Applied Mathematics (NUDT)
Xiaojun Duan: Center for Applied Mathematics (NUDT)
Bolin Zhao: Fudan University
Xue Zhang: Center for Applied Mathematics (NUDT)
Huanfei Ma: Soochow University
Jie Sun: Fudan University
Wei Lin: Fudan University

Nature Communications, 2024, vol. 15, issue 1, 1-13

Abstract: Abstract Recently, machine learning methods, including reservoir computing (RC), have been tremendously successful in predicting complex dynamics in many fields. However, a present challenge lies in pushing for the limit of prediction accuracy while maintaining the low complexity of the model. Here, we design a data-driven, model-free framework named higher-order Granger reservoir computing (HoGRC), which owns two major missions: The first is to infer the higher-order structures incorporating the idea of Granger causality with the RC, and, simultaneously, the second is to realize multi-step prediction by feeding the time series and the inferred higher-order information into HoGRC. We demonstrate the efficacy and robustness of the HoGRC using several representative systems, including the classical chaotic systems, the network dynamical systems, and the UK power grid system. In the era of machine learning and complex systems, we anticipate a broad application of the HoGRC framework in structure inference and dynamics prediction.

Date: 2024
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DOI: 10.1038/s41467-024-46852-1

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