# Manifold-integrated Gaussian process modeling, with applications to surrogate modeling of quark-gluon plasma simulations (Simon Mak -- Duke University)

**Starts:**4:00 pm on Thursday, May 4, 2023

**Location:**CCDS, 665 Comm Ave (Room 365)

In an era of costly scientific simulations, surrogate models have emerged as a powerful tool for facilitating scientific progress and engineering breakthroughs, e.g., discoveries on the Big Bang or developing new rocket engines for spaceflight. Such models are trained on a carefully designed set of simulation runs, and provide an efficient predictor (or “emulator”) for the costly scientific simulator. As simulation outputs become more complex, however, existing surrogate models can suffer poor predictive performance and uncertainty quantification, particularly with limited (expensive) training data. One saving grace is that the simulated response surfaces often embed low-dimensional manifold structures, which represent dominant physics that dictate the physical phenomenon.
We thus propose two models that leverage such manifold structures for accurate predictive modeling with limited data. The first is the Gaussian Process Subspace (GPS) model, a Bayesian nonparametric model for predicting subspace-valued functions. Such functions are widely encountered in parametric reduced order modeling, where each parameter is associated with an optimal subspace for projection-based numerical simulators. This GPS induces a joint probability model on the Grassmann manifold, and admits an analytical posterior predictive distribution that facilitates efficient subspace prediction. We explore the performance of the GPS in simulations and a microthruster application. The second is a new Additive Multi-Index Gaussian process (AdMIn-GP) model, which leverages a flexible additive structure on low-dimensional manifold embeddings of the parameter space. These embedded structures (capturing dominant multi-physics) can be efficiently estimated via a carefully constructed variational inference approach, and its integration facilitates accurate predictions in high dimensions with limited data. We show the effectiveness of the AdMIn-GP via a suite of experiments and an application to the surrogate modeling of the quark-gluon plasma, which filled the Universe shortly after the Big Bang.