PINN-FORM: A new physics-informed neural network for reliability analysis with partial differential equation

The first-order reliability method (FORM) is commonly used in the field of structural reliability analysis, which transforms the reliability analysis problem into the solution of an optimization problem with equality constraint. However, when the limit state functions (LSFs) in mechanical and engineering problems are complex, particularly for implicit partial differential equations (PDEs), FORM encounters computation difficulty and incurs unbearable computational effort. In this study, the physics-informed neural network (PINN), which is a new branch of deep learning technology for addressing forward and inverse problems with PDEs, is applied as a black-box solution tool. For LSFs with implicit PDE expressions, PINN-FORM is constructed by combining PINN with FORM, which can avoid the calculation of the real structure response. Moreover, a loss function model with an optimization target item is established. Then, an adaptive weight strategy, which can balance the interplay between different parts of the loss function, is suggested to enhance the predictive accuracy. To demonstrate the effectiveness of PINN-FORM, five benchmark examples with LSFs expressed by implicit PDEs, including two-dimensional and three-dimensional problems, and steady state and transient state problems are tested. The results illustrate the proposed PINN-FORM not only is very accurate, but also can simultaneously predict the solutions of PDEs and reliability index within a single training process.