A Sample-Efficient Moment-Matching Monte Carlo (MM-MC) Framework for Ultra High-Dimensional Uncertainty Analysis

Accurate uncertainty quantification (UQ) is essential for estimating the probability of failure and analyzing system safety. The classical Monte Carlo (MC) method serves as a benchmark for solving such complex problems, owing to its ability to capture distribution tail behavior and handle any initial distribution. However, the performance of MC simulation for UQ depends on sample size. Surrogate methods are problem-specific and require reformulation, whereas standard moment-matching methods account only for the first four moments-at the expense of higher-order moments-rendering them ineffective for reliability analysis involving rare events. This article introduces the Moment-Matching Monte Carlo (MM-MC) method. The backbone of the proposed method relies on the one-time offline computation of the weights and scaling factors; this calculation relies on an optimization aimed at matching higher-order statistical moments while minimizing the impact of cross-moments. The problem-independent scaling factors and weights can then be used to solve any UQ problem in real time, demonstrating the generalizability of the MM-MC framework to a wide range of UQ applications. Several test cases are solved using a very limited number of data points. The method is thus particularly well-suited for large-scale, safety-critical systems operating in real-time with highly constrained computational resources.