Deep Inverse Rosenblatt Transport for Structural Reliability Analysis

Abstract: Accurately estimating the probability of failure in engineering systems under uncertainty is a fundamental challenge, particularly in high-dimensional settings and for rare events. Conventional reliability analysis methods often become computationally intractable or exhibit high estimator variance when applied to problems with hundreds of uncertain parameters or highly concentrated failure regions. In this work, we investigate the use of the recently proposed Deep Inverse Rosenblatt Transport (DIRT) framework for reliability analysis in solid mechanics. DIRT combines a TT decomposition with an inverse Rosenblatt transformation to construct a low-rank approximation of the posterior distribution, enabling efficient sampling and probability estimation in high-dimensional spaces. By representing the optimal importance density in the TT format, DIRT scales linearly in the input dimension while maintaining a compact, reusable surrogate of the target distribution. We demonstrate the effectiveness of the DIRT framework on three analytical reliability problems and one numerical example with dimensionality ranging from 2 to 250. Compared to established methods such as Bayesian updating with Subset Simulation (BUS-SuS), DIRT seems to lower the estimator variance while accurately capturing rare event probabilities for the benchmark problems of this study.