TY - JOUR
T1 - A gradient-enhanced sparse grid algorithm for uncertainty quantification
AU - de Baar, Jouke H.S.
AU - Harding, Brendan
N1 - Publisher Copyright:
© 2015 by Begell House, Inc.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - High-dimensional surrogates
KW - Sparse grids
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=84945264462&partnerID=8YFLogxK
U2 - 10.1615/Int.J.UncertaintyQuantification.2015014394
DO - 10.1615/Int.J.UncertaintyQuantification.2015014394
M3 - Article
SN - 2152-5080
VL - 5
SP - 453
EP - 468
JO - International Journal for Uncertainty Quantification
JF - International Journal for Uncertainty Quantification
IS - 5
ER -