Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces
Author(s)
Constantine, Paul G.; Wang, Qiqi; Dow, Eric A.
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Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace---of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction.
Date issued
2014-07Department
Massachusetts Institute of Technology. Department of Aeronautics and AstronauticsJournal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Constantine, Paul G., Eric Dow, and Qiqi Wang. “Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces.” SIAM Journal on Scientific Computing 36, no. 4 (January 2014): A1500–A1524. © 2014 Society for Industrial and Applied Mathematics
Version: Final published version
ISSN
1064-8275
1095-7197