The Annals of Applied Statistics

Calibrating a large computer experiment simulating radiative shock hydrodynamics

Robert B. Gramacy, Derek Bingham, James Paul Holloway, Michael J. Grosskopf, Carolyn C. Kuranz, Erica Rutter, Matt Trantham, and R. Paul Drake

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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.

Article information

Source
Ann. Appl. Stat. Volume 9, Number 3 (2015), 1141-1168.

Dates
Received: October 2014
Revised: June 2015
First available in Project Euclid: 2 November 2015

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1446488734

Digital Object Identifier
doi:10.1214/15-AOAS850

Mathematical Reviews number (MathSciNet)
MR3418718

Zentralblatt MATH identifier
06525981

Keywords
Emulator tuning nonparametric regression big data local Gaussian process mesh adaptive direct search (MADS) modularization

Citation

Gramacy, Robert B.; Bingham, Derek; Holloway, James Paul; Grosskopf, Michael J.; Kuranz, Carolyn C.; Rutter, Erica; Trantham, Matt; Drake, R. Paul. Calibrating a large computer experiment simulating radiative shock hydrodynamics. Ann. Appl. Stat. 9 (2015), no. 3, 1141--1168. doi:10.1214/15-AOAS850. http://projecteuclid.org/euclid.aoas/1446488734.


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