Elastic Bayesian Model Calibration

Journal Article · 17 February 2025 · SIAM/ASA Journal on Uncertainty Quantification

DOI: https://doi.org/10.1137/24m1644092 · OSTI ID:2532367

Francom, Devin ^[1]; Tucker, J. Derek  ^[2]; Huerta, Gabriel ^[2]; Shuler, Kurtis ^[2]; Ries, Daniel ^[2]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

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. In conclusion, 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001; NA0003525
• OSTI ID: 2532367
• Report Number(s): LA-UR--24-29605
• Journal Information: SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 1 Vol. 13; ISSN 2166-2525
• Publisher: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
• Country of Publication: United States
• Language: English