PARALLEL PARTIAL EMULATION IN APPLICATIONS

Abstract

Emulators are used to approximate the output of large computer simulations. Statistical emulators are surrogates that, in addition to predicting the mean behavior of the system, provide an estimate of the error in that prediction. Classical Gaussian Stochastic Process emulators predict scalar outputs based on a modest number of input parameters. To make predictions across a space-time field of input variables is not feasible using classical Gaussian process methods. Parallel Partial Emulation is a new statistical emulator methodology that predicts a field of outputs at space-time locations, based on a set of input parameters of modest dimension. Parallel partial emulation is constructed as a Gaussian process in parameter space, but no correlation in space/time is assumed. Thus the computational work of parallel partial emulation scales as the cube of the number of input parameters (as traditional Gaussian Process emulation) and linearly with space-time grid. The behavior of Parallel Partial Emulation predictions in complex applications is not well understood. Scientists would like to understand how predictions depend on the separation of input parameters, across the space-time outputs. It is also of interest to study whether the emulator predictions inherit properties (e.g conservation) from the numerical simulator. This paper studies the properties of emulator predictions, in the context of scalar and systems of partial differential equation.