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

doi:10.1088/1674-1056/ad12a8

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

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