Harnessing physics-informed operators for high-dimensional reliability analysis problems

Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly and time-consuming, especially when dealing with systems governed by complex physical laws which necessitates computationally intensive numerical methods such as finite element or finite volume techniques. On the other hand, surrogate-based methods offer an efficient alternative for computing reliability by approximating the underlying model from limited data. Neural operators have recently emerged as effective surrogates for modelling physical systems governed by partial differential equations. These operators can learn solutions to PDEs for varying inputs and parameters. Here, we investigate the efficacy of the recently developed physics-informed wavelet neural operator in solving reliability analysis problems. In particular, we investigate the possibility of using physics-informed operator for solving high-dimensional reliability analysis problems, while bypassing the need for any simulation. Through four numerical examples, we illustrate that physics-informed operator can seamlessly solve high-dimensional reliability analysis problems with reasonable accuracy, while eliminating the need for running expensive simulations.