The evaluation of failure probability for complex engineering system is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and therefore requires numerous repeated simulations of the failure model to generate sufficient samples. To improve the efficiency, methods based on surrogate models are proposed to approximate the limit state function. In this work, we reframe the approximation of the limit state function as an operator learning problem and utilize the DeepONet framework with a hybrid approach to estimate the failure probability. Numerical results show that our proposed method outperforms the prior neural hybrid method.

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