Active learning attraction basins of dynamical system

doi:10.1088/1674-1056/adbede

中国物理B ›› 2025, Vol. 34 ›› Issue (5): 58901-058901.doi: 10.1088/1674-1056/adbede

所属专题： SPECIAL TOPIC — Computational programs in complex systems

Active learning attraction basins of dynamical system

Xiao-Wei Cao(曹小尾)¹, Xiao-Lei Ru(茹小磊)^1,2,†, and Gang Yan(严钢)^1,2,‡

1 MOE Key Laboratory of Advanced Micro-Structured Materials, and School of Physical Science and Engineering, Tongji University, Shanghai 200092, China;
2 National Key Laboratory of Autonomous Intelligent Unmanned Systems, MOE Frontiers Science Center for Intelligent Autonomous Systems, and Shanghai Research Institute of Intelligence Science and Technology, Tongji University, Shanghai 200092, China

收稿日期:2024-12-02 修回日期:2025-03-02 接受日期:2025-03-11 出版日期:2025-05-15 发布日期:2025-04-18
通讯作者: Xiao-Lei Ru, Gang Yan E-mail:ruxiaolei@qq.com;gyan@tongji.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. T2225022, 12350710786, 62088101, and 12161141016), Shuguang Program of Shanghai Education Development Foundation (Grant No. 22SG21), Shanghai Municipal Education Commission, and the Fundamental Research Funds for the Central Universities.

Active learning attraction basins of dynamical system

Xiao-Wei Cao(曹小尾)¹, Xiao-Lei Ru(茹小磊)^1,2,†, and Gang Yan(严钢)^1,2,‡

1 MOE Key Laboratory of Advanced Micro-Structured Materials, and School of Physical Science and Engineering, Tongji University, Shanghai 200092, China;
2 National Key Laboratory of Autonomous Intelligent Unmanned Systems, MOE Frontiers Science Center for Intelligent Autonomous Systems, and Shanghai Research Institute of Intelligence Science and Technology, Tongji University, Shanghai 200092, China

Received:2024-12-02 Revised:2025-03-02 Accepted:2025-03-11 Online:2025-05-15 Published:2025-04-18
Contact: Xiao-Lei Ru, Gang Yan E-mail:ruxiaolei@qq.com;gyan@tongji.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. T2225022, 12350710786, 62088101, and 12161141016), Shuguang Program of Shanghai Education Development Foundation (Grant No. 22SG21), Shanghai Municipal Education Commission, and the Fundamental Research Funds for the Central Universities.

摘要/Abstract

摘要： Dynamical systems often exhibit multiple attractors representing significantly different functioning conditions. A global map of attraction basins can offer valuable guidance for stabilizing or transitioning system states. Such a map can be constructed without prior system knowledge by identifying attractors across a sufficient number of points in the state space. However, determining the attractor for each initial state can be a laborious task. Here, we tackle the challenge of reconstructing attraction basins using as few initial points as possible. In each iteration of our approach, informative points are selected through random seeding and are driven along the current classification boundary, promoting the eventual selection of points that are both diverse and enlightening. The results across various experimental dynamical systems demonstrate that our approach requires fewer points than baseline methods while achieving comparable mapping accuracy. Additionally, the reconstructed map allows us to accurately estimate the minimum escape distance required to transition the system state to a target basin.

关键词: complex system, attraction basin, active learning

Abstract: Dynamical systems often exhibit multiple attractors representing significantly different functioning conditions. A global map of attraction basins can offer valuable guidance for stabilizing or transitioning system states. Such a map can be constructed without prior system knowledge by identifying attractors across a sufficient number of points in the state space. However, determining the attractor for each initial state can be a laborious task. Here, we tackle the challenge of reconstructing attraction basins using as few initial points as possible. In each iteration of our approach, informative points are selected through random seeding and are driven along the current classification boundary, promoting the eventual selection of points that are both diverse and enlightening. The results across various experimental dynamical systems demonstrate that our approach requires fewer points than baseline methods while achieving comparable mapping accuracy. Additionally, the reconstructed map allows us to accurately estimate the minimum escape distance required to transition the system state to a target basin.

Key words: complex system, attraction basin, active learning

中图分类号: (Complex systems)

89.75.-k

05.45.-a (Nonlinear dynamics and chaos) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

Xiao-Wei Cao(曹小尾), Xiao-Lei Ru(茹小磊), and Gang Yan(严钢). Active learning attraction basins of dynamical system[J]. 中国物理B, 2025, 34(5): 58901-058901.

Xiao-Wei Cao(曹小尾), Xiao-Lei Ru(茹小磊), and Gang Yan(严钢). Active learning attraction basins of dynamical system[J]. Chin. Phys. B, 2025, 34(5): 58901-058901.

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Active learning attraction basins of dynamical system

Active learning attraction basins of dynamical system

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