A neural network solution of first-passage problems  

作　　者：Jiamin QIAN Lincong CHEN J.Q.SUN 

机构地区：[1]College of Civil Engineering,Huaqiao University,Xiamen,361021,Fujian Province,China [2]Department of Mechanical Engineering,University of California,Merced,CA,95343,USA

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第11期2023-2036,共14页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11972070,12072118,and 12372029);the Natural Science Funds for Distinguished Young Scholars of the Fujian Province of China(No.2021J06024)。

摘　　要：This paper proposes a novel method for solving the first-passage time probability problem of nonlinear stochastic dynamic systems.The safe domain boundary is exactly imposed into the radial basis function neural network(RBF-NN)architecture such that the solution is an admissible function of the boundary-value problem.In this way,the neural network solution can automatically satisfy the safe domain boundaries and no longer requires adding the corresponding loss terms,thus efficiently handling structure failure problems defined by various safe domain boundaries.The effectiveness of the proposed method is demonstrated through three nonlinear stochastic examples defined by different safe domains,and the results are validated against the extensive Monte Carlo simulations(MCSs).

关 键 词：first-passage time probability nonlinear stochastic dynamic system radial basis function neural network(RBF-NN) safe domain boundary Monte Carlo simulation(MCS) 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O211.6[自动化与计算机技术—控制科学与工程]