New preprint is out: AK-MCS-C²: Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation, a joint work with Vincent Chabridon (EDF R&D) and Mathilde Mougeot (ENS Paris-Saclay).

Active-learning reliability methods such as AK-MCS estimate the probability that an engineering system fails by training a Gaussian process surrogate and enriching it with new evaluations near the limit-state surface. Classical enrichment rules (the U-function, the Expected Feasibility Function) rely on the surrogate’s Gaussian posterior, whose uncertainty estimates carry no distribution-free guarantee. In this work we replace that model-dependent uncertainty measure with cross-conformal prediction sets (the J+GP and J-minmax-GP estimators, see my prior work on conformal prediction): they drive the selection of new points, yield certified two-sided bounds on the failure probability, and provide a coverage diagnostic that can be tracked throughout the active-learning run on analytical examples.

The figure shows where each method places its evaluations on the 2D four-branch benchmark: all three concentrate effort along the failure boundary, with the conformal variants reaching comparable accuracy at a similar evaluation budget. Across different benchmarks the conservative J-minmax-GP variant recovers the reference failure probability while keeping empirical coverage on or above the nominal level even as adaptive sampling breaks the exchangeability the guarantee assumes.

The paper comes with a reproducible Python library: EdgarJaber/AK-MCS-C2.