Computing large deviation prefactors of stochastic dynamical systems based on machine learning

doi:10.1088/1674-1056/ad12a8

中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/ad12a8

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

收稿日期:2023-06-19 修回日期:2023-11-28 接受日期:2023-12-06 出版日期:2024-03-19 发布日期:2024-04-01
通讯作者: Shenglan Yuan E-mail:shenglanyuan@hust.edu.cn
基金资助:
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).

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

Received:2023-06-19 Revised:2023-11-28 Accepted:2023-12-06 Online:2024-03-19 Published:2024-04-01
Contact: Shenglan Yuan E-mail:shenglanyuan@hust.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: machine learning, large deviation prefactors, stochastic dynamical systems, rare events

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.

Key words: machine learning, large deviation prefactors, stochastic dynamical systems, rare events

中图分类号: (Computational methods in statistical physics and nonlinear dynamics)

05.10.-a

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)

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[J]. 中国物理B, 2024, 33(4): 40501-040501.

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Computing large deviation prefactors of stochastic dynamical systems based on machine learning

Computing large deviation prefactors of stochastic dynamical systems based on machine learning

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