On Active Learning for Gaussian Process-based Global Sensitivity Analysis

TL;DR

This paper introduces a novel active learning strategy called MUSIC for efficiently estimating Sobol indices in global sensitivity analysis using Gaussian process surrogates, demonstrating faster convergence in low dimensions.

Contribution

The paper proposes a new active learning method, MUSIC, that focuses on main effects to improve Sobol index convergence, outperforming existing strategies in low-dimensional settings.

Findings

MUSIC converges faster than existing methods in low-dimensional problems.

Performance of MUSIC is comparable to random sampling in high-dimensional problems.

Demonstrated effectiveness of the method in a practical wind tunnel experiment.

Abstract

This paper explores the application of active learning strategies to adaptively learn Sobol indices for global sensitivity analysis. We demonstrate that active learning for Sobol indices poses unique challenges due to the definition of the Sobol index as a ratio of variances estimated from Gaussian process surrogates. Consequently, learning strategies must either focus on convergence in the numerator or the denominator of this ratio. However, rapid convergence in either one does not guarantee convergence in the Sobol index. We propose a novel strategy for active learning that focuses on resolving the main effects of the Gaussian process (associated with the numerator of the Sobol index) and compare this with existing strategies based on convergence in the total variance (the denominator of the Sobol index). The new strategy, implemented through a new learning function termed the MUSIC (minimize uncertainty in Sobol index convergence), generally converges in Sobol index error more rapidly than the existing strategies based on the Expected Improvement for Global Fit (EIGF) and the Variance Improvement for Global Fit (VIGF). Both strategies are compared with simple sequential random sampling and the MUSIC learning function generally converges most rapidly for low-dimensional problems. However, for high-dimensional problems, the performance is comparable to random sampling. The new learning strategy is demonstrated for a practical case of adaptive experimental design for large-scale Boundary Layer Wind Tunnel experiments.