A physics-based emulator for the simulation of geophysical mass flows
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Rare natural hazards such as large volcanic eruptions can cause loss of life and damage to property. With sufficient information, those charged with public safety may issue warnings of impending hazards, to mitigate the hazard impact. Recent developments in modeling and simulating large geophysical mass flows can provide useful information in assessing hazard risk. These computer simulations of a system of partial differential equations are expensive to run, but analysis based on a few simulations is not sufficiently accurate for hazard analysis. Computational costs can be reduced by constructing a statistical emulator—a regression surface for selected output variables derived from several full simulator runs. Whenever the result from a simulation is required in an analysis, the emulator can be queried quickly. A key feature of the emulator is that an estimate of the prediction uncertainty, or error, is defined together with the regression estimate. A popular emulator is the Gaussian Process emulator, or GaSP, which is constructed as the mean of a Bayesian posterior distribution over input parameters. In this work, we propose an alternative procedure for constructing emulators, one that uses knowledge about the model physics. We model the mass flow as an Ornstein-Uhlenbeck (OU) process for sliding blocks along a surface, a stochastic extension of Newton's law of motion. We demonstrate how the OU results can be used to predict simulator results. A fit to the OU process is made, together with an error approximation, by classical statistical techniques.