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A neural network solution of first-passage problems

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A neural network solution of first-passage problems
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).

first-passage time probabilitynonlinear stochastic dynamic systemradial basis function neural network(RBF-NN)safe domain boundaryMonte Carlo simulation(MCS)

Jiamin QIAN、Lincong CHEN、J.Q.SUN

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College of Civil Engineering,Huaqiao University,Xiamen 361021,Fujian Province,China

Department of Mechanical Engineering,University of California,Merced,CA 95343,U.S.A.

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

2024

10.1007/s10483-024-3189-8

应用数学和力学(英文版)
上海大学

应用数学和力学(英文版)

影响因子：0.294
ISSN：0253-4827
年,卷(期)：2024.45(11)