Elastic Bayesian Model Calibration

TL;DR

This paper presents a Bayesian calibration framework for functional data that accounts for both amplitude and phase variations, improving model accuracy in scientific applications involving misaligned functional responses.

Contribution

It introduces a novel approach to Bayesian calibration that separates amplitude and phase variations in functional data, enabling more accurate model-data alignment.

Findings

Effective calibration of functional models with phase and amplitude variations.

Successful application to material science experiments.

Improved model-data matching in simulated and real data.

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.