Calibrating a large computer experiment simulating radiative shock hydrodynamics

Abstract

We consider adapting a canonical computer model calibration apparatus, involving coupled Gaussian process (GP) emulators, to a computer experiment simulating radiative shock hydrodynamics that is orders of magnitude larger than what can typically be accommodated. The conventional approach calls for thousands of large matrix inverses to evaluate the likelihood in an MCMC scheme. Our approach replaces that costly ideal with a thrifty take on essential ingredients, synergizing three modern ideas in emulation, calibration and optimization: local approximate GP regression, modularization, and mesh adaptive direct search. The new methodology is motivated both by necessity - considering our particular application - and by recent trends in the supercomputer simulation literature. A synthetic data application allows us to explore the merits of several variations in a controlled environment and, together with results on our motivating real-data experiment, lead to noteworthy insights into the dynamics of radiative shocks as well as the limitations of the calibration enterprise generally.

Published at http://dx.doi.org/10.1214/15-AOAS850 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Composite Gaussian process models for emulating expensive functions
• GPfit: An R package for Gaussian Process Model Fitting using a New Optimization Algorithm
• Accurate emulators for large-scale computer experiments
• Parallelizing Gaussian Process Calculations in R
• Local Gaussian process approximation for large computer experiments
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