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Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise |
Linghongzhi Lu(陆凌弘志)1, Yang Li(李扬)2, and Xianbin Liu(刘先斌)1,† |
1 State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China |
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Abstract Massive data from observations, experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models. We present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussian α-stable Lévy noise. More explicitly, firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers-Moyal formulas. Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process. Three examples are then given to demonstrate the feasibility. This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.
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Received: 09 October 2022
Revised: 17 November 2022
Accepted manuscript online: 02 December 2022
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PACS:
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05.10.-a
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(Computational methods in statistical physics and nonlinear dynamics)
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05.10.Gg
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(Stochastic analysis methods)
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12172167), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). |
Corresponding Authors:
Xianbin Liu
E-mail: xbliu@nuaa.edu.cn
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Cite this article:
Linghongzhi Lu(陆凌弘志), Yang Li(李扬), and Xianbin Liu(刘先斌) Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise 2023 Chin. Phys. B 32 050501
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[1] Sun J C 2016 Chin. Phys. Lett. 33 100503 [2] Yan X and Wu Y 2012 Chin. Phys. Lett. 29 128901 [3] Xu W, Wang L, Feng J, Qiao Y and Han P 2018 Chin. Phys. B 27 110503 [4] Jordan M I and Mitchell T M 2015 Science 349 255 [5] Marx V 2013 Nature 498 255 [6] Williams M O, Kevrekidis I G and Rowley C W 2015 J. Nonlinear Sci. 25 1307 [7] Schmid P J 2010 J. Fluid Mech. 656 5 [8] Boninsegna L, Nüske F and Clementi C 2018 J. Chem. Phys. 148 241723 [9] Brunton S L, Proctor J L and Kutz J N 2016 Proc. Natl. Acad. Sci. USA 113 3932 [10] Schaeffer H, Caisch R, Hauck C D and Osher S 2013 Proc. Natl. Acad. Sci. USA 110 6634 [11] Rudy S, Alla A, Brunton S L and Kutz J N 2019 SIAM J. Appl. Dyn. Syst. 18 643 [12] Chen R T Q, Rubanova Y, Bettencourt J and Duvenaud D K 2018 Advances in Neural Information Processing Systems (Curran Associates, Inc.) Vol. 31 [13] Li X, Wong T K L, Chen R T and Duvenaud D 2020 Proceedings of Machine Learning Research (PMLR) Vol. 118, pp. 1-28 [14] Garcia C A, Otero A, Felix P, Presedo J and Marquez D G 2017 Phys. Rev. E 96 022104 [15] Ruttor A, Batz P and Opper M 2013 Advances in Neural Information Processing Systems (Curran Associates, Inc.) Vol. 26 [16] Ditlevsen P D 1999 Geophys. Res. Lett. 26 1441 [17] Raser J M and O'shea E K 2005 Science 309 2010 [18] Jourdain B, Méléard S and Woyczynski W A 2012 J. Math. Biol. 65 677 [19] Zoia A, Rosso A and Kardar M 2007 Phys. Rev. E 76 021116 [20] Matthäus F, Mommer M S, Curk T and Dobnikar J 2011 PloS One 6 e18623 [21] Humphries N E, Queiroz N, Dyer J R, et al. 2010 Nature 465 1066 [22] Ramos-Fernández G, Mateos J L, Miramontes O, Cocho G, Larralde H and Ayala-Orozco B 2004 Behav. Ecol. Sociobiol. 55 223 [23] Li Y and Duan J 2021 Physica D 417 132830 [24] Li Y and Duan J 2022 J. Stat. Phys. 186 1 [25] Li Y, Duan J, Liu X and Zhang Y 2020 Chaos 30 063142 [26] Rosenkrantz R D 2012 ET Jaynes: Papers on probability, statistics and statistical physics (Berlin: Springer Science & Business Media) Vol. 158 [27] Huang R Z, Liao H J, Liu Z Y, Xie H D, Xie Z Y, Zhao H H, Chen J and Xiang T 2018 Chin. Phys. B 27 070501 [28] Zhang J P, Guo H M, Jing W J and Jin Z 2019 Acta Phys. Sin. 68 150501 (in Chinese) [29] Radovic A, Williams M, Rousseau D, Kagan M, Bonacorsi D, Himmel A, Aurisano A, Terao K and Wongjirad T 2018 Nature 560 41 [30] Carrasco Kind M and Brunner R J 2013 Mon. Not. R. Astron. Soc. 432 1483 [31] Butler K T, Davies D W, Cartwright H, Isayev O and Walsh A 2018 Nature 559 547 [32] Lindsey J 1999 Biometrics 55 1277 [33] Veillette M 2014 https://github.com/markveillette/stbl [34] Süuel G M, Garcia-Ojalvo J, Liberman L M and Elowitz M B 2006 Nature 440 545 |
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