中国物理B ›› 2025, Vol. 34 ›› Issue (4): 40505-040505.doi: 10.1088/1674-1056/adb733

所属专题： Featured Column — COMPUTATIONAL PROGRAMS FOR PHYSICS

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Model-free prediction of chaotic dynamics with parameter-aware reservoir computing

Jianmin Guo(郭建敏)1,2, Yao Du(杜瑶)1, Haibo Luo(罗海波)1, Xuan Wang(王晅)1, Yizhen Yu(于一真)1,†, and Xingang Wang(王新刚)1   

  1. 1 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China;
    2 College of Physics and Electronic Information Engineering, Qinghai Normal University, Xining 810008, China
  • 收稿日期:2024-12-27 修回日期:2025-02-15 接受日期:2025-02-18 出版日期:2025-04-15 发布日期:2025-04-15
  • 通讯作者: Yizhen Yu E-mail:yzyu@snnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12275165). XGW was also supported by the Fundamental Research Funds for the Central Universities (Grant No. GK202202003).

Model-free prediction of chaotic dynamics with parameter-aware reservoir computing

Jianmin Guo(郭建敏)1,2, Yao Du(杜瑶)1, Haibo Luo(罗海波)1, Xuan Wang(王晅)1, Yizhen Yu(于一真)1,†, and Xingang Wang(王新刚)1   

  1. 1 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China;
    2 College of Physics and Electronic Information Engineering, Qinghai Normal University, Xining 810008, China
  • Received:2024-12-27 Revised:2025-02-15 Accepted:2025-02-18 Online:2025-04-15 Published:2025-04-15
  • Contact: Yizhen Yu E-mail:yzyu@snnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12275165). XGW was also supported by the Fundamental Research Funds for the Central Universities (Grant No. GK202202003).

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摘要： Model-free, data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science. Stimulated by the recent progress in machine learning, considerable attention has been given to the inference of chaos by the technique of reservoir computing (RC). In particular, by incorporating a parameter-control channel into the standard RC, it is demonstrated that the machine is able to not only replicate the dynamics of the training states, but also infer new dynamics not included in the training set. The new machine-learning scheme, termed parameter-aware RC, opens up new avenues for data-based analysis of chaotic systems, and holds promise for predicting and controlling many real-world complex systems. Here, using typical chaotic systems as examples, we give a comprehensive introduction to this powerful machine-learning technique, including the algorithm, the implementation, the performance, and the open questions calling for further studies.

关键词: chaos prediction, time-series analysis, bifurcation diagram, parameter-aware reservoir computing

Abstract: Model-free, data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science. Stimulated by the recent progress in machine learning, considerable attention has been given to the inference of chaos by the technique of reservoir computing (RC). In particular, by incorporating a parameter-control channel into the standard RC, it is demonstrated that the machine is able to not only replicate the dynamics of the training states, but also infer new dynamics not included in the training set. The new machine-learning scheme, termed parameter-aware RC, opens up new avenues for data-based analysis of chaotic systems, and holds promise for predicting and controlling many real-world complex systems. Here, using typical chaotic systems as examples, we give a comprehensive introduction to this powerful machine-learning technique, including the algorithm, the implementation, the performance, and the open questions calling for further studies.

Key words: chaos prediction, time-series analysis, bifurcation diagram, parameter-aware reservoir computing

中图分类号:  (Low-dimensional chaos)

  • 05.45.Ac
05.45.Tp (Time series analysis) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence) 89.75.-k (Complex systems)