Spline-Based Emulators for Radiative Shock Experiments With Measurement Error

Abstract

Radiation hydrodynamics and radiative shocks are of fundamental interest in the high-energy-density physics research due to their importance in understanding astrophysical phenomena such as supernovae. In the laboratory, experiments can produce shocks with fundamentally similar physics on reduced scales. However, the cost and time constraints of the experiment necessitate use of a computer algorithm to generate a reasonable number of outputs for making valid inference. We focus on modeling emulators that can efficiently assimilate these two sources of information accounting for their intrinsic differences. The goal is to learn how to predict the breakout time of the shock given the information on associated parameters such as pressure and energy. Under the framework of the Kennedy–O’Hagan model, we introduce an emulator based on adaptive splines. Depending on the preference of having an interpolator for the computer code output or a computationally fast model, a couple of different variants are proposed. Those choices are shown to perform better than the conventional Gaussian-process-based emulator and a few other choices of nonstationary models. For the shock experiment dataset, a number of features related to computer model validation such as using interpolator, necessity of discrepancy function, or accounting for experimental heterogeneity are discussed, implemented, and validated for the current dataset. In addition to the typical Gaussian measurement error for real data, we consider alternative specifications suitable to incorporate noninformativeness in error distributions, more in agreement with the current experiment. Comparative diagnostics, to highlight the effect of measurement error model on predictive uncertainty, are also presented. Supplementary materials for this article are available online.

KEY WORDS:

• Adaptive spline
• Computer model validation
• Emulator
• Measurement error model
• Non-Gaussian error
• Reversible jump Markov chain Monte Carlo

Acknowledgments

This work was funded by the Predictive Sciences Academic Alliances Program in DOE/NNSA-ASC via grant DEFC52- 08NA28616. The authors thank the editors and referees for their insightful feedback and for helping to improve the content and presentation of this article.