Augmenting a Simulation Campaign for Hybrid Computer Model and Field Data Experiments

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, that is, 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.

Keywords:

• Gaussian processes
• Integrated mean squared error
• Inverse problem
• Sequential design

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work supported, in part, by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of High Energy Physics, Scientific Discovery through Advanced Computing (SciDAC) program under Award Number 0000231018; and by National Science Foundation award CMMI-2152679. Research presented in this article was also supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under project number 20220188DR. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).