Adaptive Physics-Informed Neural Network Based Directional Sampling Method for Efficient Reliability Analysis

To efficiently estimate the failure probability for structures with performance function governed by the partial differential equation, this paper proposed an adaptive physics-informed neural network based directional sampling (A-PINN-DS) method. The proposed A-PINN-DS possesses both the low dependence on labeled data from PINN and the high failure domain exploring efficiency from DS. In the proposed method, DS is firstly employed to generate the random input target collocation sample pool (TCSP) with high failure domain exploring efficiency. Then in TCSP, the neural network is trained by the partial differential physics information governing the performance function, and the neural network trained to be convergent in TCSP is used to predict the performance function response of TCSP, on which the failure probability can be estimated by DS. Because the proposed method only uses partial differential physics information instead of finite element simulation to train neural network in the TCSP for predicting performance function, it remarkably reduces the computational cost for estimating failure probability. To improve the efficiency of training PINN in TCSP, this paper designs a strategy of adaptively updating loss weights and a convergence distinguishing strategy for training PINN. Finally, the feasibility and superiority of the proposed method are verified by several examples.