Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma
This work addresses the challenge of high-dimensional surrogate modeling with limited data for physicists studying the QGP, representing an incremental improvement by incorporating domain-specific prior knowledge into a flexible Bayesian framework.
The authors tackled the problem of building accurate surrogate models for the computationally expensive simulation of the Quark-Gluon Plasma (QGP) by proposing the Additive Multi-Index Gaussian process (AdMIn-GP) model, which leverages additive structures on low-dimensional embeddings guided by multiphysics knowledge, and demonstrated considerably improved performance over existing models in numerical experiments and the QGP application.
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 very 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., multiphysics), each involving a small number of latent parameters. The AdMIn-GP models for such embedded structures 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.