A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields
Abstract
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving a mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: S543 - S562
DOI: 10.1137/16M1082688
ISSN (online): 1095-7197
Copyright
© 2017, Society for Industrial and Applied Mathematics.
History
Submitted: 5 July 2016
Accepted: 21 March 2017
Published online: 26 October 2017
Keywords
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Authors
Funding Information
U.S. Department of Energy https://doi.org/10.13039/100000015 : DE-AC52-07NA27344
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