TY - JOUR

T1 - A physics-based emulator for the simulation of geophysical mass flows

AU - Mahmood, Asif

AU - Wolpert, Robert L.

AU - Pitman, E. Bruce

N1 - Funding Information:
The work of this author was supported in part by NSF DMS-1228317, PHY-0941373, and NASA NNX09AK60G. The work of this author was supported in part by NSF grants DMS-0757367 and DMS-1228217.
Funding Information:
∗Received by the editors February 13, 2013; accepted for publication (in revised form) May 26, 2015; published electronically July 21, 2015. The genesis of this work was a 2006-07 year-long program on Development, Assessment, and Utilization of Computer Models held at the Statistical and Applied Mathematical Sciences Institute, which is supported in part by the National Science Foundation. http://www.siam.org/journals/juq/3/90944.html †Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17403 (aum54@psu.edu). The research reported herein is part of the doctoral dissertation of this author, from the University at Buffalo. ‡Department of Statistical Science, Duke University, Durham, NC 27708 (wolpert@stat.duke.edu). The work of this author was supported in part by NSF DMS–1228317, PHY–0941373, and NASA NNX09AK60G. §Department of Mathematics, University at Buffalo, Buffalo, NY 14260 (pitman@buffalo.edu). The work of this author was supported in part by NSF grants DMS–0757367 and DMS–1228217.
Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics Publications. All rights reserved.

PY - 2015

Y1 - 2015

N2 - 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. In particular, computer simulations of a model system of PDEs, which determines flow depth and runout, are expensive to run. On the other hand, analysis based on only a few simulations is not sufficiently accurate for hazard analysis. Computational costs can be reduced by constructing a statistical emulator-an approximate response 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 is defined together with the regression estimate. A popular emulator is the Gaussian Separable Process emulator, or GaSP, which is constructed as the mean of a Bayesian posterior distribution over outputs. 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 over the topography. We demonstrate how the OU results can be used to predict simulator results. By calibrating certain input parameters, a fit to the OU process is made, together with an error approximation, by classical statistical techniques, to provide an emulator of the runout computed by the computer simulator.

AB - 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. In particular, computer simulations of a model system of PDEs, which determines flow depth and runout, are expensive to run. On the other hand, analysis based on only a few simulations is not sufficiently accurate for hazard analysis. Computational costs can be reduced by constructing a statistical emulator-an approximate response 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 is defined together with the regression estimate. A popular emulator is the Gaussian Separable Process emulator, or GaSP, which is constructed as the mean of a Bayesian posterior distribution over outputs. 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 over the topography. We demonstrate how the OU results can be used to predict simulator results. By calibrating certain input parameters, a fit to the OU process is made, together with an error approximation, by classical statistical techniques, to provide an emulator of the runout computed by the computer simulator.

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U2 - 10.1137/130909445

DO - 10.1137/130909445

M3 - Article

AN - SCOPUS:85051867693

SN - 2166-2525

VL - 3

SP - 562

EP - 585

JO - SIAM-ASA Journal on Uncertainty Quantification

JF - SIAM-ASA Journal on Uncertainty Quantification

IS - 1

ER -