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Gradient-Enhanced Universal Kriging for Uncertainty Propagation Brian A. Lockwood

Summary: Gradient-Enhanced Universal Kriging for Uncertainty Propagation
Brian A. Lockwood
and Mihai Anitescu
November 14, 2010
Preprint ANL/MCS-P1808-1110
In this work, we investigate the issue of providing a statistical model for the response of a computer
model-described nuclear engineering system, for use in uncertainty propagation. The motivation behind
our approach is the need for providing an uncertainty assessment even in the circumstances where only
a few samples are available. Building on our recent work in using a regression approach with derivative
information for approximating the system response, we investigate the ability of a universal gradient-
enhanced Kriging model to provide a means for inexpensive uncertainty quantification. The universal
Kriging model can be viewed as a hybrid of polynomial regression and Gaussian process regression.
For this model, the mean behavior of the surrogate is determined by a polynomial regression, and
deviations from this mean are represented as a Gaussian process. Tests with explicit functions and
nuclear engineering models show that the universal gradient-enhanced Kriging model provides a more
accurate surrogate model when compared to either regression or ordinary Kriging models. In addition
we investigate the ability of the Kriging model to provide error predictions and bounds for regression
Keywords uncertainty quantification; Gaussian process; derivative; universal Kriging, nuclear engi-


Source: Anitescu, Mihai - Mathematics and Computer Science Division, Argonne National Laboratory
Argonne National Laboratory, Mathematics and Computer Science Division (MCS)


Collections: Computer Technologies and Information Sciences; Mathematics