A new gradient-free active subspace estimation method with application to rare event probability estimation

2026-03-31

AI Summary

This study addresses the high computational cost of estimating rare-event probabilities in the presence of high-dimensional random parameters by proposing a sequential, gradient-free active subspace estimation method. The approach iteratively constructs Kriging surrogate models in a rotated coordinate system, dynamically updates the active subspace, and integrates it into an importance sampling density learning framework, thereby enabling joint optimization of dimensionality reduction and sampling strategy. In contrast to existing methods that rely on static active subspaces, this work introduces an adaptive sequential framework that significantly enhances both the accuracy and stability of subspace estimation. Numerical benchmarks demonstrate that the proposed method achieves more accurate rare-event probability estimates at substantially lower computational cost compared to state-of-the-art alternatives.

Abstract

To reduce the cost of estimating the probability of a rare event involving a very large number of random parameters, we propose a new strategy for dimension reduction coupled with a surrogate model for the expensive part of the algorithm. To this end, we extend the Ordinary Kriging Active Subspace (OK-AS) method into a sequential version. Our approach consists of iteratively re-estimating the active subspace using a Kriging surrogate trained in a rotated coordinate system until the active subspace stabilises. This method allows for a reduction in prediction error and a better approximation of the active subspace on a benchmark of test problems. Furthermore, we integrate our algorithm into an efficient pre-existing approach for estimating the probability of a rare event. This approach is based on learning the active subspace associated with the random event whose probability is to be estimated. The sequential learning of an importance sampling density is necessary and corresponds to the expensive part of this strategy. To circumvent this issue, we integrate our sequential OK-AS version into the estimation of the importance sampling density. The numerical results indicate that our method allows for reducing the cost required to obtain a precise estimate of the rare event probability.

Problem

• rare event probability estimation
• dimension reduction
• active subspace
• computational cost
• importance sampling

Innovation

• gradient-free
• active subspace
• sequential Kriging
• rare event probability
• importance sampling