Proposal-Guided Greedy Surrogate Refinement for PDE-Driven High-Dimensional Rare-Event Estimation

TL;DR

This paper introduces a surrogate-assisted adaptive importance sampling method that locally refines surrogates along evolving proposals to efficiently estimate rare events in high-dimensional PDE problems.

Contribution

It proposes a novel local surrogate refinement framework guided by greedy latent-space sample selection, improving efficiency in high-dimensional rare-event estimation.

Findings

Achieves accuracy comparable to true-model adaptive importance sampling.

Requires substantially fewer high-fidelity evaluations.

Effective in PDE-driven problems up to 100 dimensions.

Abstract

Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive importance sampling provides a natural localization tool: its evolving proposal distribution progressively identifies the failure-relevant region. Motivated by this observation, we propose a surrogate-assisted adaptive importance sampling framework that refines the surrogate locally along the evolving proposal, rather than over the entire input space. The surrogate combines an encoder with a neural network, providing a low-dimensional latent representation for both prediction and sample selection. At each adaptive iteration, candidates drawn from the current proposal are selected by a greedy latent-space rule balancing proximity to the estimated failure boundary and sample diversity. The selected samples are evaluated by the high-fidelity model and used to refine the surrogate, which then guides the subsequent cross-entropy-type adaptive proposal update. We establish one-step proposal stability bounds under local surrogate errors, together with surrogate-induced misclassification and finite-sample estimation error bounds. Numerical experiments on multimodal benchmarks and PDE-driven rare-event problems up to 100 dimensions show that the proposed method achieves accuracy comparable to true-model adaptive importance sampling while requiring substantially fewer high-fidelity evaluations.