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

A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions