Local Gaussian Process Approximation for Large Computer Experiments

TLDR

We provide a new approach to approximate emulation of large computer experiments. The method constructs local sequential designs that dynamically select a subset of data for a Gaussian process predictor and supplies fast sequential updates for the predictive equations. Applying the local design across a predictive grid yields a trivially parallel, multicore‑efficient global predictor that outperforms compactly supported covariance methods in two large‑scale examples. Supplementary materials are available online.

Abstract

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the support of a Gaussian process predictor based on a local subset of the data. We further derive expressions for fast sequential updating of all needed quantities as the local designs are built up iteratively. Then we show how independent application of our local design strategy across the elements of a vast predictive grid facilitates a trivially parallel implementation. The end result is a global predictor able to take advantage of modern multicore architectures, providing a nonstationary modeling feature as a bonus. We demonstrate our method on two examples using designs with thousands of data points, and compare to the method of compactly supported covariances. Supplementary materials for this article are available online.