Applied Mathematics and Mechanics >
A neural network solution of first-passage problems
Received date: 2024-07-18
Online published: 2024-10-30
Supported by
the National Natural Science Foundation of China(11972070);the National Natural Science Foundation of China(12072118);the National Natural Science Foundation of China(12372029);the Natural Science Funds for Distinguished Young Scholars of the Fujian Province of China(2021J06024);Project supported by the National Natural Science Foundation of China (Nos. 11972070, 12072118, and 12372029) and the Natural Science Funds for Distinguished Young Scholars of the Fujian Province of China (No. 2021J06024)
Copyright
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).
Jiamin QIAN, Lincong CHEN, J. Q. SUN . A neural network solution of first-passage problems[J]. Applied Mathematics and Mechanics, 2024 , 45(11) : 2023 -2036 . DOI: 10.1007/s10483-024-3189-8
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