Elastic Multi-Fidelity Bayesian Model Calibration
Abstract
Bayesian calibration of functional-output computer models typically relies on dimension reduction techniques, such as functional principal component analysis, which assume that differences among simulator realizations arise only from amplitude variation. When simulator output also exhibits phase variation such as shifts in the timing or location of key features, this assumption is violated. Recent work has addressed this issue through elastic calibration, which aligns functional computer model realizations with observed experimental data prior to dimension reduction. Separately, multi-fidelity methods reduce the cost of calibration by supplementing a small number of expensive high-fidelity simulator runs with a larger ensemble of cheap low-fidelity runs. This is typically done through either a mapping strategy, which corrects low-fidelity predictions toward high-fidelity output, or a fusion strategy, which builds a shared basis across both fidelities. This paper combines these two lines of work, introducing elastic multi-fidelity Bayesian model calibration, which aligns high- and low-fidelity functional output to a common reference before applying multi-fidelity mapping or fusion. On a synthetic two-dimensional calibration problem and a dynamic material properties equation-of-state problem, both elastic multi-fidelity strategies match or improve on the leave-one-out predictive accuracy of a mono-fidelity elastic emulator, with the fusion approach achieving the lowest error. Both strategies also produce tighter calibrated posteriors than the mono-fidelity baseline, with the fusion approach providing the best coverage and parameter estimates closest to the true values.
Related
- Bayesian Calibration with Functional Outputs Using Elastic Partial Matching
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BibTeX
@misc{tucker2026elastic,
title = {{Elastic Multi-Fidelity Bayesian Model Calibration}},
author = {J. Derek Tucker and Gavin Collins and Gabriel Huerta and Justin L. Brown},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27174},
eprint = {2609.27174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27174},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Elastic Multi-Fidelity Bayesian Model Calibration
AU - J. Derek Tucker
AU - Gavin Collins
AU - Gabriel Huerta
AU - Justin L. Brown
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27174
UR - https://arxiv.org/abs/2609.27174
AB - Bayesian calibration of functional-output computer models typically relies on dimension reduction techniques, such as functional principal component analysis, which assume that differences among simulator realizations arise only from amplitude variation. When simulator output also exhibits phase variation such as shifts in the timing or location of key features, this assumption is violated. Recent work has addressed this issue through elastic calibration, which aligns functional computer model realizations with observed experimental data prior to dimension reduction. Separately, multi-fidelity methods reduce the cost of calibration by supplementing a small number of expensive high-fidelity simulator runs with a larger ensemble of cheap low-fidelity runs. This is typically done through either a mapping strategy, which corrects low-fidelity predictions toward high-fidelity output, or a fusion strategy, which builds a shared basis across both fidelities. This paper combines these two lines of work, introducing elastic multi-fidelity Bayesian model calibration, which aligns high- and low-fidelity functional output to a common reference before applying multi-fidelity mapping or fusion. On a synthetic two-dimensional calibration problem and a dynamic material properties equation-of-state problem, both elastic multi-fidelity strategies match or improve on the leave-one-out predictive accuracy of a mono-fidelity elastic emulator, with the fusion approach achieving the lowest error. Both strategies also produce tighter calibrated posteriors than the mono-fidelity baseline, with the fusion approach providing the best coverage and parameter estimates closest to the true values.
ER -