Additive Multi-Index Gaussian process modeling, with application to
  multi-physics surrogate modeling of the quark-gluon plasma
Kevin Li Simon Mak J. -F Paquet Steffen A. Bass
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.