CONFORMAL APPROACH TO GAUSSIAN PROCESS SURROGATE EVALUATIONWITH MARGINAL COVERAGE GUARANTEES

Gaussian processes (GPs) are a Bayesian machine learning (ML) approach widely used to construct surrogate models for the uncertainty quantification (UQ) of computer simulation codes in industrial applications. It provides both a mean predictor and an estimate of the posterior prediction variance, the latter being used to produce Bayesian credibility intervals. Interpreting these intervals relies on the Gaussianity of the simulation model and the well-specification of the priors, which may not be appropriate. We propose to address this issue with the help of conformal prediction (CP), which is a finite-sample and distribution-free technique for estimating prediction intervals with marginal coverage guarantees. In the present work, a method for building adaptive cross-conformal prediction intervals is proposed by weighting the nonconformity score with the posterior standard deviation of the GP. The resulting CP intervals exhibit a level of adaptivity akin to Bayesian credibility sets and display a significant correlation with surrogate model local approximation error while being free from the underlying model assumptions and having marginal frequentist coverage guarantees. These estimators can be used to evaluate the quality of a GP surrogate model and can assist a decisionmaker in choosing the best prior to the specific application of the GP. We illustrate the proposed method's performance through a panel of numerical examples based on various computer experiments, including the GP metamodeling of analytical functions and an expensive-to-evaluate simulator of the clogging phenomenon in steam generators of nuclear reactors.