The use of the Karhunen Loève expansion in the design of computer experiments

Abstract

This article proposes the use of the Karhunen Loève expansion in the design of computer experiments when the Gaussian Process (GP) model is used to model the output, Y(x). We start by finding the K-L expansion in the case of the univariate and multivariate processes. When the analytical solution does not exist, we apply several methods of approximation, such as Haar wavelet functions and Fourier expansions. Numerical examples are presented to illustrate the idea of the approximations. We use the approximated model to select the maximum entropy sampling design.