  Evaluating failure probability for complex engineering systems is a
computationally intensive task. While the Monte Carlo method is easy to
implement, it converges slowly and, hence, requires numerous repeated
simulations of a complex system 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. The
numerical results show that our proposed method outperforms the prior neural
hybrid method.
