Computer emulation with non-stationary Gaussian processes

TL;DR

This paper introduces a non-stationary Gaussian process emulator for computer experiments, improving modeling of local features like discontinuities and peaks, and aiding better input point selection.

Contribution

It proposes a novel non-stationary GP model based on two nested stationary GPs, enhancing local feature handling and input selection in emulation.

Findings

Superior handling of local features like jumps and peaks.

Improved selection of future input points near boundaries.

Outperforms traditional stationary GP emulators.

Abstract

Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input variables, a GP emulator trained on finitely many runs of the experiment also offers error bars for response surface estimates at unseen input values. This helps select future input values where the experiment should be run to minimize the uncertainty in the response surface estimation. However, traditional GP emulators use stationary covariance functions, which perform poorly and lead to sub-optimal selection of future input points when the response surface has sharp local features, such as a jump discontinuity or an isolated tall peak. We propose an easily implemented non-stationary GP emulator, based on two stationary GPs, one nested into the other, and demonstrate its superior ability in handling local features and selecting future input points from the boundaries of such features.