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
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.
Fund: 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.
Corresponding Authors:
Xiao-Lei Ru, Gang Yan
E-mail: ruxiaolei@qq.com;gyan@tongji.edu.cn
Cite this article:
Xiao-Wei Cao(曹小尾), Xiao-Lei Ru(茹小磊), and Gang Yan(严钢) Active learning attraction basins of dynamical system 2025 Chin. Phys. B 34 058901
[1] Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V, Held H, Nes E V, Rietkerk M and Sugihara G 2009 Nature 461 53 [2] Menck P J, Heitzig J, Marwan N and Kurths J 2013 Nat. Phys. 9 89 [3] Cornelius S P, Kath W L and Motter A E 2013 Nat. Commun. 4 1942 [4] Zhang B C, Li L, Yang S J, Wang S H, Zha Z J and Huang Q M 2020 Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, June 13-19, 2020, Seattle, USA, p. 8756 [5] Ren P Z, Xiao Y, Chang X J, Huang P Y, Li Z H, Gupta B B, Chen X J and Wang X 2021 ACM Comput. Surv. 9 180 [6] Kirsch A, Amersfoort J V, Gal Y 2019 33rd International Conference on Neural Information Processing Systems, December 8-14, 2019, Vancouver, Canada, p. 7026 [7] Che Y M and Cheng C Q 2021 Chaos 31 053129 [8] Roy M, Mandal S, Hens C, Prasad A, Kuznetsov N V and Shrimali M D 2022 Chaos 32 101104 [9] Gauthier D J, Fischer I and Röhm A 2022 Chaos 32 113107 [10] Du Y, Li Q, Fan H, Zhan M, Xiao J H and Wang X G 2024 Phys. Rev. Res. 6 013181 [11] Campbell C, Cristianini N and Smola A 2000 Proceedings of the 17th International Conference on Machine Learning,June 29-July 2, 2000, Stanford, USA, p. 111 [12] Tong S and Koller D 2001 J. Mach. Learn. Res. 2 45 [13] Brinker K 2003 Proceedings of the 20th International Conference on Machine Learning, August 21-24, 2003, Washington, USA, p. 59 [14] Zhu J J and Bento J 2017 arXiv:1702.07956 [cs-LG] [15] Mayer C and Timofte R 2020 IEEE Winter Conference on Applications of Computer Vision, March 1-5, 2020, Snowmass, USA, p. 3071 [16] Ducoffe M and Precioso F 2018 arXiv:1802.09841 [cs-LG] [17] Munjal P, Hayat N, Hayat M, Sourati J and Khan S 2022 Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, June 21-24, 2022, New Orleans, USA, p. 223 [18] Zhu L, Liu Z and Han S 2019 33rd International Conference on Neural Information Processing Systems, December 8-14, 2019, Vancouver, Canada, p. 14774 [19] Moosavi-Dezfooli S M, Fawzi A and Frossard P 2016 Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, June 27-30, 2016, Las Vegas, USA, p. 2574 [20] Barkema G T and Mousseau N 1996 Phys. Rev. Lett. 77 4358 [21] Draxler F, Veschgini K, Salmhofer M and Hamprecht F 2018 Proceedings of the 35th International Conference on Machine Learning, July 10-15, 2018, Stockholmsmässan, Sweden, p. 1309 [22] Daza A, Wagemakers A, Georgeot B, Guéry-Odelin D and Sanjuán M A F 2016 Sci. Rep. 6 31416 [23] Sener O and Savarese S 2018 6th International Conference on Learning Representations, April 30-May 3, 2018, Vancouver, Canda, p. 1 [24] Wang D and Shang Y 2014 International Joint Conference on Neural Networks, July 6-11, 2014, Beijing, China, p. 112 [25] Ash J T, Zhang C C, Krishnamurthy A, Langford J and Agarwal A 2020 8th International Conference on Learning Representations, April 26-May 1, 2020, Virtual Only Conference, p. 1 [26] Sanhedrai H, Gao J X, Bashan A, Schwartz M, Havlin S and Barzel B 2022 Nat. Phys. 18 338 [27] Zhang X, Zhang X, Yan G and Moore J M 2023 Phys. Rev. Res. 5 033138 [28] Yan G, Ren J, Lai Y C, Lai C H and Li B W 2012 Phys. Rev. Lett. 108 218703 [29] Klinshov V V, Nekorkin V I and Kurths J 2015 New J. Phys. 18 013004
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
