Input Subspace Detection for Dimension Reduction in High Dimensional Approximation

Details Input Subspace Detection for Dimension Reduction in High Dimensional Approximation Input Subspace Detection for Dimension Reduction in High Dimensional Approximation

2012-02-16

arxiv.org/abs/1202.3508v1

Mathematics

Numerical Analysis

Scientific paper

Many multivariate functions encountered in practice vary primarily along a few directions in the space of input parameters. When these directions correspond with coordinate directions, one may apply global sensitivity measures to determine the parameters with the greatest contribution to the function's variability. 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 for detecting the directions of variability of a function using evaluations of its derivative with respect to the input parameters. We demonstrate how to exploit these directions to construct a surrogate function that depends on fewer variables than the original function, thus reducing the dimension of the original problem. We apply this procedure to an exercise in uncertainty quantification using an elliptic PDE with a model for the coefficients that depends on 250 independent parameters. The dimension reduction procedure identifies a 5-dimensional subspace suitable for constructing surrogates.

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