Parallel partial Gaussian process emulation for computer models with massive output

Abstract

We consider the problem of emulating (approximating) computer models (simulators) that produce massive output. The specific simulator we study is a computer model of volcanic pyroclastic flow, a single run of which produces up to $10^{9}$ outputs over a space–time grid of coordinates. An emulator (essentially a statistical model of the simulator—we use a Gaussian Process) that is computationally suitable for such massive output is developed and studied from practical and theoretical perspectives. On the practical side, the emulator does unexpectedly well in predicting what the simulator would produce, even better than much more flexible and computationally intensive alternatives. This allows the attainment of the scientific goal of this work, accurate assessment of the hazards from pyroclastic flows over wide spatial domains. Theoretical results are also developed that provide insight into the unexpected success of the massive emulator. Generalizations of the emulator are introduced that allow for a nugget, which is useful for the application to hazard assessment.