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arXiv · 2606.20191

AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation

Edgar Jaber·Vincent Chabridon·Mathilde Mougeot
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Abstract

We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.

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Edgar Jaber, Vincent Chabridon, Mathilde Mougeot. 2026-06-18. AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation. https://arxiv.org/abs/2606.20191

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