A Graphical Multi-Fidelity Gaussian Process Model, with Application to Emulation of Heavy-Ion Collisions

Abstract

With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of different fidelities to train an efficient predictive model which emulates the expensive simulator. For complex scientific problems and with careful elicitation from scientists, such multi-fidelity data may often be linked by a directed acyclic graph (DAG) representing its scientific model dependencies. We thus propose a new Graphical Multi-fidelity Gaussian Process (GMGP) model, which embeds this DAG structure (capturing scientific dependencies) within a Gaussian process framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable algorithm for recursive computation of the posterior mean and variance along at each depth level of the DAG. We also present a novel experimental design methodology over the DAG given an experimental budget, and propose a nonlinear extension of the GMGP via deep Gaussian processes. The advantages of the GMGP are then demonstrated via a suite of numerical experiments and an application to emulation of heavy-ion collisions, which can be used to study the conditions of matter in the Universe shortly after the Big Bang. The proposed model has broader uses in data fusion applications with graphical structure, which we further discuss.

Keywords:

• Computer experiments
• Gaussian processes
• Graphical models
• Multi-fidelity modeling
• Nuclear physics

Acknowledgments

We also thank the JETSCAPE collaboration (https://jetscape.org/) for insightful conversations and discussions.

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

1 The fit with a Matérn kernel here yielded poor results, hence, our use of the squared-exponential kernel.

Additional information

Funding

The authors gratefully acknowledge funding from NSF CSSI 2004571, NSF DMS 2210729, NSF DMS 2316012, DE-SC0024477 (YJ, SM), and DE-FG02-05ER41367 (SAB, JFP and DS).