A Review of Bayesian Surrogate Modeling for High-Dimensional Computer Simulations
Abstract
Bayesian surrogate models play a central role in the analysis of computationally expensive physics-based simulators, particularly when uncertainty quantification (UQ) is a primary objective. This review provides a high-level overview of commonly used Bayesian surrogate modeling methods for high-dimensional computer simulations, with emphasis on both methodological foundations and practical applications. We review the advantages of Bayesian surrogates, the challenges posed by high-dimensional outputs, and two broad classes of methods: Gaussian process models, including scalable approximations, and Bayesian basis function regression approaches such as polynomial chaos expansions, Bayesian multivariate adaptive regression splines, Bayesian projection pursuit regression, and Bayesian additive regression trees. We also review strategies for handling high-dimensional simulator outputs, of which dimension-reduction approaches based on low-dimensional output representations are most common. Finally, we highlight key applications of Bayesian surrogate modeling in forward UQ, global sensitivity analysis, and Bayesian model calibration, and demonstrate a practical workflow utilizing these methods in simulated and real data analyses. We conclude by identifying open challenges and future research directions related to method selection, computational scalability, predictive accuracy, and UQ fidelity.
Related
- Isotonic surrogate modeling for computer experiments with many input variables
- Accelerating droplet-laden Stokes flow simulations with hierarchical surrogate modeling
- BGM-IV: AI-Powered Bayesian Generative Modeling for Instrumental Variable Regression with High-Dimensional Covariates
- Bayesian uncertainty quantification of the ignition behavior of a HEFA-SPK surrogate
- Variational Filtering for Bayesian Last Layers with an Independent Binary Probit Surrogate
BibTeX
@misc{collins2026review,
title = {{A Review of Bayesian Surrogate Modeling for High-Dimensional Computer Simulations}},
author = {Gavin Collins and Gabriel Huerta and J. Derek Tucker and Kellin Rumsey},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31870},
eprint = {2610.31870},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31870},
}
RIS
TY - UNPB
TI - A Review of Bayesian Surrogate Modeling for High-Dimensional Computer Simulations
AU - Gavin Collins
AU - Gabriel Huerta
AU - J. Derek Tucker
AU - Kellin Rumsey
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31870
UR - https://arxiv.org/abs/2610.31870
AB - Bayesian surrogate models play a central role in the analysis of computationally expensive physics-based simulators, particularly when uncertainty quantification (UQ) is a primary objective. This review provides a high-level overview of commonly used Bayesian surrogate modeling methods for high-dimensional computer simulations, with emphasis on both methodological foundations and practical applications. We review the advantages of Bayesian surrogates, the challenges posed by high-dimensional outputs, and two broad classes of methods: Gaussian process models, including scalable approximations, and Bayesian basis function regression approaches such as polynomial chaos expansions, Bayesian multivariate adaptive regression splines, Bayesian projection pursuit regression, and Bayesian additive regression trees. We also review strategies for handling high-dimensional simulator outputs, of which dimension-reduction approaches based on low-dimensional output representations are most common. Finally, we highlight key applications of Bayesian surrogate modeling in forward UQ, global sensitivity analysis, and Bayesian model calibration, and demonstrate a practical workflow utilizing these methods in simulated and real data analyses. We conclude by identifying open challenges and future research directions related to method selection, computational scalability, predictive accuracy, and UQ fidelity.
ER -