Elastic Bayesian Model Calibration
Abstract.
Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. We demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.
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Title of paper: Elastic Bayesian Model Calibration
Authors: Devin Francom, J. Derek Tucker, Gabriel Huerta, Kurtis Shuler and Daniel Ries
File: Supplement.pdf
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Information & Authors
Information
Published In
SIAM/ASA Journal on Uncertainty Quantification
Pages: 195 - 227
DOI: 10.1137/24M1644092
ISSN (online): 2166-2525
Copyright
© 2025 Society for Industrial and Applied Mathematics and American Statistical Association.
History
Submitted: 5 March 2024
Accepted: 20 September 2024
Published online: 18 February 2025
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Funding Information
U.S. Department of Energy (DOE): DE-NA0003525
Funding: This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. This work was supported by the NA-22 program, the Advanced Simulation and Computing program, and Laboratory Directed Research and Development program at Los Alamos National Laboratory and Sandia National Laboratories. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
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