Global sensitivity analysis using low-rank tensor approximations

TL;DR

This paper introduces a low-cost method for global sensitivity analysis using low-rank tensor approximations to efficiently compute Sobol' indices, especially in high-dimensional models, and validates its effectiveness through various applications.

Contribution

The paper presents a novel approach to evaluate Sobol' indices via low-rank tensor meta-models, reducing computational effort compared to traditional methods.

Findings

Indices converge faster with increasing sample size

Method compares favorably to polynomial chaos expansions

Validated on structural mechanics and heat conduction models

Abstract

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model.