A Framework for Controlling Sources of Inaccuracy in Gaussian Process Emulation of Deterministic Computer Experiments

TL;DR

This paper develops a comprehensive framework for designing experiments that improve the accuracy of Gaussian process emulators in deterministic computer simulations, balancing various sources of inaccuracy.

Contribution

It introduces principles for experimental design that optimize accuracy and robustness in Gaussian process emulation, addressing issues like space-filling and non-stationarity.

Findings

Space-filling properties improve nominal and numeric accuracy.

Non-stationarity requires denser sampling in certain regions.

The framework provides practical guidelines for input selection.

Abstract

Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with limited time and resources. Principles of experimental design are proposed and justified which ensure high nominal, numeric, and parameter estimation accuracy for Gaussian process emulation of deterministic simulations. The space-filling properties "small fill distance" and "large separation distance" are only weakly conflicting and ensure well-controlled nominal, numeric, and parameter estimation error, while non-stationarity requires a greater density of experimental inputs in regions of the input space with more quickly decaying correlation. This work will provide scientists and engineers with robust, rigorously justified, and practically useful overarching principles for selecting combinations of simulation inputs with high information content.