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

• URL: http://arxiv.org/abs/2306.11418v1
• Date: Tue, 20 Jun 2023 09:59:45 GMT
• Title: Computing large deviation prefactors of stochastic dynamical systems based on machine learning
• Authors: Yang Li, Shenglan Yuan, Linghongzhi Lu, Xianbin Liu
• Abstract summary: We present large deviation theory that characterizes the exponential estimate for rare events of dynamical systems in the limit of weak noise. We design a neural network framework to compute quasipotential, most probable paths and prefactors based on the decomposition of vector field. Numerical experiments demonstrate its powerful function in exploring internal mechanism of rare events triggered by weak random fluctuations.
• Score: 4.474127100870242
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more accurate calculation of mean exit time via computing large deviation prefactors with the research efforts 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 vector field. We corroborate the higher effectiveness and accuracy of our algorithm with a practical example. Numerical experiments demonstrate its powerful function in exploring internal mechanism of rare events triggered by weak random fluctuations.

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