Spatiotemporal-dependent reliability analysis with adaptive sampling physics-informed neural networks

Balancing accuracy and computational efficiency remains a challenge for simulation-based time-dependent reliability analysis (TRA) under uncertainty. Traditional TRA methods often fall short in focusing solely on fixed hotspot(s) of complex engineering systems, neglecting the dynamic nature of potential failure regions, such as moving hotspots. To address these limitations, this paper proposes a spatiotemporal-dependent reliability analysis (STDRA) framework for engineering systems governed by partial differential equations (PDEs). Key contributions include: (1) resolving incompleteness by employing a physics-informed neural network (PINN) to calculate global performance across all spatiotemporal “spots†in the investigated PDE system; (2) enabling STDRA by deriving results through Monte Carlo simulations of the PINN-based framework, without the need for design of experiment (DoE) samples; and (3) enhancing accuracy and efficiency through a novel adaptive spatiotemporal sampling (ASTS) strategy, which optimally trains the PINN by focusing on critical spatial and temporal domains. The proposed ASTS-PINN-based STDRA framework is validated using a 2D isotropic elastic plate and a complex laser cladding process, showcasing its superiority over existing state-of-the-art TRA methods.