On Active Learning for Gaussian Process-based Global Sensitivity
  Analysis
Mohit Chauhan Mariel Ojeda-Tuz Ryan Catarelli Kurtis Gurley Dimitrios Tsapetis Michael D. Shields
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.