Simulation-free reliability analysis with active learning and Physics-Informed Neural Network

Physical phenomena are often described by partial differential equations (PDEs), which have been traditionally solved using computationally demanding finite element, difference, or volume methods to produce labeled data. Due to its multi-query nature, characterization of event probabilities requires many such simulations, which can become prohibitive given the high costs of acquiring labeled data. As opposed to conventional PDE solution methods, Physics-Informed Neural Network (PINN) is directly trained using the physics knowledge encoded in PDEs, and therefore is simulation free. Building on this capability, we propose a simulation-free uncertainty quantification method called adaptively trained PINN for reliability analysis (AT-PINN-RA). We introduce an active learning approach with the dual objective of training PINN for solving PDEs and characterizing the limit state. The approach actively learns from the responses of the PINN model to identify the limit state and sub-sequently, adaptively shifts the focus of the training of the PINN model to regions of high importance for failure probability characterization to boost the accuracy and efficiency of reliability estimation. The performance of AT-PINN-RA is investigated using four benchmark problems with varying complexities. In all examples, AT-PINN-RA provides accurate estimates of event probabilities with high efficiency.