Elastic Bayesian Model Calibration
Devin Francom, J. Derek Tucker, Gabriel Huerta, Kurtis Shuler, and, Daniel Ries

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…
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Taxonomy
TopicsProbabilistic and Robust Engineering Design · Advanced Multi-Objective Optimization Algorithms · Model Reduction and Neural Networks
