Additive Multi-Index Gaussian Process Modeling, with Application to Multi-Physics Surrogate Modeling of the Quark-Gluon Plasma

• 成果类型: Article; Early Access
• 署名作者: Li, Kevin; Mak, Simon; Paquet, J. -F; Bass, Steffen A.
• 署名单位: Duke University; Vanderbilt University; Vanderbilt University; Duke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2529025
• 发表日期: 2025
• 关键词: active subspace; computer; prediction; Emulation; reduction

摘要

The Quark-Gluon Plasma (QGP) is a unique phase of nuclear matter, theorized to have filled the Universe shortly after the Big Bang. A critical challenge in studying the QGP is that, to reconcile experimental observables with theoretical parameters, one requires many simulation runs of a complex physics model over a high-dimensional parameter space. Each run is computationally expensive, requiring thousands of CPU hours, thus limiting physicists to only several hundred runs. Given limited training data for high-dimensional prediction, existing surrogate models often yield poor predictions with high predictive uncertainties, leading to imprecise scientific findings. To address this, we propose a new Additive Multi-Index Gaussian process (AdMIn-GP) model, which leverages a flexible additive structure on low-dimensional embeddings of the parameter space. This is guided by prior scientific knowledge that the QGP is dominated by multiple distinct physical phenomena (i.e., multi-physics), each involving a small number of latent parameters. The AdMIn-GP models for such embedded structure within a flexible Bayesian nonparametric framework, which facilitates efficient model fitting via a carefully constructed variational inference approach with inducing points. We show the effectiveness of the AdMIn-GP via a suite of numerical experiments and our QGP application, where we demonstrate considerably improved surrogate modeling performance over existing models. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.