Computing exit location distribution of stochastic dynamical systems with noncharacteristic boundary based on deep learning

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL
Yang Li , Feng Zhao , Jianlong Wang , Shengyuan Xu
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引用次数: 0

Abstract

Rare events induced by random perturbations are ubiquitous phenomena in natural systems, where the exit location distribution is a significant quantity, and its computation is challenging. In this study, we compute the exit location distribution of stochastic dynamical systems with weak Gaussian noise for a noncharacteristic boundary based on deep learning and large deviation theory. First, we introduce the perturbation expressions of the prefactor and exit location distribution via Wentzel–Kramers–Brillouin approximation. We then design a deep learning method to compute the quasipotential, the prefactor, and the exit location distribution. Two examples are described to verify the effectiveness of the proposed algorithm. The findings of this study are expected to provide valuable insights into exploring the mechanisms of rare events triggered by random fluctuations.

基于深度学习计算具有非特征边界的随机动力系统的出口位置分布
随机扰动诱发的罕见事件是自然系统中无处不在的现象,其中出口位置分布是一个重要的量,其计算具有挑战性。在本研究中,我们基于深度学习和大偏差理论,计算了具有弱高斯噪声的非特征边界随机动力学系统的出口位置分布。首先,我们通过 Wentzel-Kramers-Brillouin 近似引入了前因子和出口位置分布的扰动表达式。然后,我们设计了一种深度学习方法来计算准位势、前因子和出口位置分布。我们通过两个实例来验证所提算法的有效性。本研究的发现有望为探索随机波动引发罕见事件的机制提供有价值的见解。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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