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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015014394
pages 453-468

A GRADIENT-ENHANCED SPARSE GRID ALGORITHM FOR UNCERTAINTY QUANTIFICATION

Jouke H. S. de Baar
Mathematical Sciences Institute, Australian National University, John Dedman Building 27, Union Lane, Canberra, ACT, 2601, Australia
Brendan Harding
Mathematical Sciences Institute, Australian National University, John Dedman Building 27, Union Lane, Canberra, ACT, 2601, Australia

ABSTRACT

Adjoint-based gradient information has been successfully incorporated to create surrogate models of the output of expensive computer codes. Exploitation of these surrogates offers the possibility of uncertainty quantification, optimization and parameter estimation at reduced computational cost. Presently, when we look for a surrogate method to include gradient information, the most common choice is gradient-enhanced Kriging (GEK). As a competitor, we develop a novel method: gradient-enhanced sparse grid interpolation. Results for two test functions, the Rosenbrock function and a test function based on the drag of a transonic airfoil with random shape deformations, show that the gradient-enhanced sparse grid interpolation is a reliable surrogate that can incorporate the gradient information efficiently for high-dimensional problems.