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Chin. Phys. B, 2024, Vol. 33(4): 040501    DOI: 10.1088/1674-1056/ad12a8
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Computing large deviation prefactors of stochastic dynamical systems based on machine learning

Yang Li(李扬)1, Shenglan Yuan(袁胜兰)2,3,†, Linghongzhi Lu(陆凌宏志)4, and Xianbin Liu(刘先斌)4
1 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China;
2 Department of Mathematics, School of Sciences, Great Bay University, Dongguan 523000, China;
3 Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China;
4 State Key Laboratory of Mechanics and Control for Aerospace Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract  We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise. We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning. More specifically, we design a neural network framework to compute quasipotential, most probable paths and prefactors based on the orthogonal decomposition of a vector field. We corroborate the higher effectiveness and accuracy of our algorithm with two toy models. Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
Keywords:  machine learning      large deviation prefactors      stochastic dynamical systems      rare events  
Received:  19 June 2023      Revised:  28 November 2023      Accepted manuscript online:  06 December 2023
PACS:  05.10.-a (Computational methods in statistical physics and nonlinear dynamics)  
  05.10.Gg (Stochastic analysis methods)  
  05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)  
  02.50.-r (Probability theory, stochastic processes, and statistics)  
Fund: Project supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20220917) and the National Natural Science Foundation of China (Grant Nos. 12001213 and 12302035).
Corresponding Authors:  Shenglan Yuan     E-mail:  shenglanyuan@hust.edu.cn

Cite this article: 

Yang Li(李扬), Shenglan Yuan(袁胜兰), Linghongzhi Lu(陆凌宏志), and Xianbin Liu(刘先斌) Computing large deviation prefactors of stochastic dynamical systems based on machine learning 2024 Chin. Phys. B 33 040501

[1] Ma J, Xu Y, Li Y, Tian R, Ma S and Kurths J 2021 Appl. Math. Mech. 42 65
[2] Zheng Y, Yang F, Duan J, Sun X, Fu L and Kurths J 2020 Chaos 30 013132
[3] Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V, Held H, Van Nes E H, Rietkerk M and Sugihara G 2009 Nature 461 53
[4] Dykman M I, Mori E, Ross J and Hunt P 1994 J. Chem. Phys. 100 5735
[5] Yuan S, Li Y and Zeng Z 2022 Math. Model. Nat. Pheno. 17 34
[6] Yuan S, Zeng Z and Duan J 2021 J. Stat. Mech. Theory E 2021 033204
[7] Zhu W and Wu Y 2003 Nonlinear Dyn. 32 291
[8] Zhang Y, Jin Y, Xu P and Xiao S 2020 Nonlinear Dyn. 99 879
[9] Freidlin M I and Wentzell A D 2012 Random Perturbations of Dynamical Systems (Berlin:Springer)
[10] Grafke T, Schäfer T and Vanden-Eijnden E 2021 arXiv:2103.04837[cond-mat.stat-mech]
[11] Schorlepp T, Grafke T and Grauer R 2021 J. Phys. A:Math. Theor. 54 235003
[12] Bouchet F and Reygner J 2022 J. Stat. Phys. 189 21
[13] Schorlepp T, Grafke T and Grauer R 2023 J. Stat. Phys. 190 50
[14] Naeh T, Klosek M, Matkowsky B and Schuss Z 1990 SIAM J. Appl. Math. 50 595
[15] Matkowsky B, Schuss Z and Tier C 1983 SIAM J. Appl. Math. 43 673
[16] Matkowsky B and Schuss Z 1982 SIAM J. Appl. Math. 42 822
[17] Roy R V 1997 Int. J. Nonlin. Mech. 32 173
[18] Maier R S and Stein D L 1997 SIAM J. Appl. Math. 57 752
[19] Beri S, Mannella R, Luchinsky D G, Silchenko A and McClintock P V 2005 Phys. Rev. E 72 036131
[20] Weinan E 2017 Commun. Math. Stat. 5 1
[21] Li Y and Duan J 2021 Physica D 417 132830
[22] Li Y and Duan J 2022 J. Stat. Phys. 186 30
[23] Karniadakis G E, Kevrekidis I G, Lu L, Perdikaris P, Wang S and Yang L 2021 Nat. Rev. Phys. 3 422
[24] Rotskoff G and Vanden-Eijnden E 2018 NIPS 31 7146
[25] Opper M 2019 Annalen der Physik 531 1800233
[26] Li Y, Duan J and Liu X 2021 Phys. Rev. E 103 012124
[27] Wei W, Gao T, Chen X and Duan J 2022 Chaos 32 051102
[28] Li Y, Xu S, Duan J, Liu X and Chu Y 2022 Nonlinear Dyn. 109 1877
[29] Lin B, Li Q and Ren W 2021 PMLR 145 652
[30] Li Y, Yuan S and Xu S 2023 Commun. Nonlinear Sci. Numer. Simul. 126 107425
[31] Xu Y, Zhang H, Li Y, Zhou K, Liu Q and Kurths J 2020 Chaos 30 013133
[32] Bouchet F and Reygner J 2016 Ann. Henri Poincare 17 3499
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