Efficient failure probability calculation through mesh refinement

TL;DR

This paper introduces a mesh refinement technique to enhance hybrid surrogate methods, significantly reducing the number of costly exact model evaluations needed for failure probability calculations.

Contribution

The paper proposes a novel mesh refinement approach that improves local surrogate accuracy and efficiency in failure probability estimation.

Findings

Reduces the number of exact model evaluations

Demonstrates robustness across multiple examples

Achieves significant efficiency gains

Abstract

We present a novel way of accelerating hybrid surrogate methods for the calculation of failure probabilities. The main idea is to use mesh refinement in order to obtain improved local surrogates of low computation cost to simulate on. These improved surrogates can reduce significantly the required number of evaluations of the exact model (which is the usual bottleneck of failure probability calculations). Meanwhile the effort on evaluations of surrogates is dramatically reduced by utilizing low order local surrogates. Numerical results of the application of the proposed approach in several examples of increasing complexity show the robustness, versatility and gain in efficiency of the method.