Augmenting a simulation campaign for hybrid computer model and field data experiments

TL;DR

This paper develops a new IMSPE-based acquisition strategy for the Kennedy and O'Hagan calibration framework, improving the efficiency of simulation campaigns by optimally selecting simulator data points.

Contribution

It derives a closed-form IMSPE criterion and gradient for sequential data acquisition within the KOH calibration framework, enhancing data efficiency.

Findings

IMSPE-based acquisition improves simulation efficiency

Strategy concentrates sampling in calibration space

Demonstrated on benchmark problems and a chemical extraction application

Abstract

The Kennedy and O'Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its ``knobs" (calibration inputs) to best match observations from a real physical/field experiment and correct for any modeling bias (second GP) when predicting under new field conditions (design inputs). There are well-established methods for placement of design inputs for data-efficient planning of a simulation campaign in isolation, i.e., without field data: space-filling, or via criterion like minimum integrated mean-squared prediction error (IMSPE). Analogues within the coupled GP KOH framework are mostly absent from the literature. Here we derive a closed form IMSPE criterion for sequentially acquiring new simulator data for KOH. We illustrate how acquisitions space-fill in design space, but concentrate in calibration space. Closed form IMSPE precipitates a closed-form gradient for efficient numerical optimization. We demonstrate that our KOH-IMSPE strategy leads to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on an application to equilibrium concentrations of rare earth elements for a liquid-liquid extraction reaction.