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).