A graphical multi-fidelity Gaussian process model, with application to emulation of expensive computer simulations

With advances in scientific computing and mathematical modeling, complex phenomena 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 varying accuracies (or fidelities) to train an efficient predictive model (or emulator) for the expensive simulator. In complex problems, simulation data with different fidelities are often connected scientifically via a directed acyclic graph (DAG), which cannot be integrated within existing multi-fidelity emulator models. We thus propose a new Graphical Multi-fidelity Gaussian process (GMGP) model, which embeds this scientific DAG information within a Gaussian process framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable formulation for recursively computing the posterior predictive distribution along sub-graphs. We also present an experimental design framework over the DAG given a computational budget, and propose a nonlinear extension of the GMGP model via deep Gaussian processes. The advantages of the GMGP model over existing methods 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.