Efficient computer experiment designs for Gaussian process surrogates

Due to advancements in supercomputing and algorithms for finite element analysis, today's computer simulation models often contain complex calculations that can result in a wealth of knowledge. Gaussian processes (GPs) are highly desirable models for computer experiments for their predictive accuracy and uncertainty quantification. This dissertation addresses GP modeling when data abounds as well as GP adaptive design when simulator expense severely limits the amount of collected data. For data-rich problems, I introduce a localized sparse covariance GP that preserves the flexibility and predictive accuracy of a GP's predictive surface while saving computational time. This locally induced Gaussian process (LIGP) incorporates latent design points, inducing points, with a local Gaussian process built from a subset of the data. Various methods are introduced for the design of the inducing points. LIGP is then extended to adapt to stochastic data with replicates, estimating noise while relying upon the unique design locations for computation. I also address the goal of identifying a contour when data collection resources are limited through entropy-based adaptive design. Unlike existing methods, the entropy-based contour locator (ECL) adaptive design promotes exploration in the design space, performing well in higher dimensions and when the contour corresponds to a high/low quantile. ECL adaptive design can join with importance sampling for the purpose of reducing uncertainty in reliability estimation.