Cross-Validation Based Adaptive Sampling for Multi-Level Gaussian Process Models

TL;DR

This paper introduces a multi-level adaptive sampling algorithm that optimally selects new training points across different model complexities to improve Gaussian process emulators for expensive hierarchical computer models.

Contribution

It proposes a novel cross-validation based adaptive sampling method that balances improvement and cost across multiple model levels for Gaussian process training.

Findings

Enhanced prediction accuracy at top model levels.

Efficient sampling reduces the number of costly high-level runs.

Flexible batch and single point selection strategies.

Abstract

Complex computer codes or models can often be run in a hierarchy of different levels of complexity ranging from the very basic to the sophisticated. The top levels in this hierarchy are typically expensive to run, which limits the number of possible runs. To make use of runs over all levels, and crucially improve predictions at the top level, we use multi-level Gaussian process emulators (GPs). The accuracy of the GP greatly depends on the design of the training points. In this paper, we present a multi-level adaptive sampling algorithm to sequentially increase the set of design points to optimally improve the fit of the GP. The normalised expected leave-one-out cross-validation error is calculated at all unobserved locations, and a new design point is chosen using expected improvement combined with a repulsion function. This criterion is calculated for each model level weighted by an associated cost for the code at that level. Hence, at each iteration, our algorithm optimises for both the new point location and the model level. The algorithm is extended to batch selection as well as single point selection, where batches can be designed for single levels or optimally across all levels.