Multifidelity variance reduction for pick-freeze Sobol index estimation

TL;DR

This paper introduces a multifidelity variance reduction method for efficiently estimating Sobol sensitivity indices, leveraging fast approximations to reduce computational costs in models with costly evaluations.

Contribution

The paper presents a novel multifidelity approach for variance reduction in Sobol index estimation, improving efficiency when high-fidelity model evaluations are expensive.

Findings

Significant reduction in computational cost demonstrated

Method effectively leverages low-fidelity models

Applicable to models with costly output evaluations

Abstract

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index, which can be estimated using a large sample of evaluations of the output. We propose a variance reduction technique, based on the availability of a fast approximation of the output, which can enable significant computational savings when the output is costly to evaluate.