ak-mcs-conformal-failure-probability

name	ak-mcs-conformal-failure-probability
description	Active Kriging Monte Carlo Simulation with conformal certification for failure probability estimation in structural reliability. Uses adaptive cross-conformal strategy for small-sample settings with J+GP conformal estimator. Provides distribution-free guarantees on prediction errors for improved classification near limit-state surfaces. arXiv:2606.20191. Activates: failure probability, structural reliability, active learning, kriging monte carlo, conformal prediction, AK-MCS, J+GP estimator, rare event estimation.
metadata	{"arxiv_id":"2606.20191","published":"2026-06-18","authors":"Edgar Jaber, Vincent Chabridon, Mathilde Mougeot","tags":["statistics","machine-learning","reliability","conformal","kriging","monte-carlo"]}

Context

AK-MCS-C2 integrates Active Kriging Monte Carlo Simulation (AK-MCS) with conformal prediction for failure probability estimation in structural reliability analysis. Unlike standard AK-MCS, it provides distribution-free guarantees on prediction errors.

Core Methodology

1. Build kriging surrogate (Gaussian Process) of the limit-state function
2. Apply J+GP conformal estimator for distribution-free prediction intervals
3. Adaptive cross-conformal strategy specifically designed for small-sample settings
4. Active learning loop: select most informative samples near limit-state surface
5. Improved uncertainty quantification → more reliable classification of boundary samples
6. Failure probability estimation with certified error bounds

Key Results

• Distribution-free guarantees on prediction errors (no assumptions on GP residuals)