DMS Statistics and Data Science Seminar

Speaker: Simon Mak, Duke University

Title: A graphical Gaussian process model for multi-fidelity emulation of expensive computer codes

Abstract: With advances in scientific computing, complex phenomena can now be reliably simulated via computer code. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses simulation data of varying accuracies (or fidelities) to train an efficient predictive model (or emulator) for the expensive computer simulator. In many complex applications (e.g., heavy-ion physics), simulation data with different fidelities are connected 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 underlying DAG structure within a Gaussian process predictive framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable recursive formulation for computing the posterior predictive distribution along sub-graphs. We also present a design framework for allocating experimental runs over the DAG given a computational budget. The advantages of the GMGP model over existing methods are then demonstrated via a suite of numerical experiments and an application to heavy-ion collisions, which shed light on the origins of the Universe shortly after the Big Bang.