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A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/16M1082688· OSTI ID:1438756
 [1];  [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scienti c Computing
  2. Univ. of Texas, Austin, TX (United States). Institute for Computational Engineering and Sciences
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In this paper, 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. Lastly, 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.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1438756
Report Number(s):
LLNL-JRNL--696879; LLNL-JRNL--695979
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 39; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (6)

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes journal January 2018
Multilevel approximation of Gaussian random fields: Fast simulation journal December 2019
Second-order control of complex systems with correlated synthetic data journal November 2019
Eigenvalue Problems for Exponential-Type Kernels journal January 2020
Scalable hierarchical PDE sampler for generating spatially correlated random fields using non-matching meshes preprint January 2017
Second-order Control of Complex Systems with Correlated Synthetic Data text January 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
PDEs with random input data
mixed nite elements
multilevel Monte Carlo
multilevel methods
uncertainty quanti cation