Sample correlation adjustments for robust Multi-fidelity Monte Carlo under limited pilot sampling

2026-05-21

AI Summary

This work addresses the challenge in multifidelity Monte Carlo (MFMC) estimation where scarce pilot samples lead to biased correlation coefficient estimates, thereby undermining variance reduction. To mitigate this issue, the authors propose a correction mechanism grounded in probabilistic information from the covariance matrix, enabling more robust correlation estimation under limited sample sizes. Additionally, they introduce a novel discrepancy metric and formulate a minimax optimization framework to select an estimator that minimizes expected suboptimality under the worst-case scenario. By integrating multifidelity modeling, covariance estimation, and probabilistic analysis, the proposed approach significantly enhances the accuracy and stability of MFMC estimators within a fixed computational budget. The method’s efficacy is demonstrated through numerical experiments on NASA’s entry, descent, and landing problem.

Abstract

Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the correlation coefficients between the different fidelity models which are not usually known in practice. The correlations are typically estimated using offline pilot samples and the sample correlation formula, after which the MFMC method proceeds as if the estimated correlations are the true correlations. Computational cost often restricts the number of pilot samples used leading to poor correlation estimates and suboptimal estimators. Leveraging the MFMC problem setting and probabilistic information about the sample covariance matrix, we present a method to improve standard sample-based correlation estimates in the presence of limited pilot samples. We define a novel discrepancy function quantifying the estimator suboptimality which in turn facilitates selecting a correlation estimator minimizing the worst-case expected discrepancy, where the expectation is taken with respect to the pilot sampling variability. Through a simple bivariate Gaussian example and a multi-fidelity modeling application from a NASA Entry, Descent, and Landing (EDL) problem, we show that this method produces better MFMC estimators than the standard sample covariance under small pilot sample sizes and limited total budgets.

Problem

• Multi-fidelity Monte Carlo
• correlation estimation
• limited pilot sampling
• variance reduction
• sample correlation

Innovation

• Multi-fidelity Monte Carlo
• sample correlation adjustment
• limited pilot sampling
• variance reduction
• robust estimation