Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems
Abstract
Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of samplingbased uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble when applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated KarhunenLoève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.
 Authors:

 Sandia National Lab. (SNLNM), Albuquerque, NM (United States). Center for Computing Research
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1421620
 Report Number(s):
 SAND20178877J
Journal ID: ISSN 21662525; 656365
 Grant/Contract Number:
 NA0003525
 Resource Type:
 Accepted Manuscript
 Journal Name:
 SIAM/ASA Journal on Uncertainty Quantification
 Additional Journal Information:
 Journal Volume: 6; Journal Issue: 1; Journal ID: ISSN 21662525
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; sampling methods; stochastic collocation methods; stochastic partial differential equations; anisotropic diffusion models; forward uncertainty propagation; embedded ensemble propagation
Citation Formats
D'Elia, M., Edwards, H. C., Hu, J., Phipps, E., and Rajamanickam, S. Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems. United States: N. p., 2018.
Web. doi:10.1137/16m1066324.
D'Elia, M., Edwards, H. C., Hu, J., Phipps, E., & Rajamanickam, S. Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems. United States. doi:10.1137/16m1066324.
D'Elia, M., Edwards, H. C., Hu, J., Phipps, E., and Rajamanickam, S. Thu .
"Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems". United States. doi:10.1137/16m1066324. https://www.osti.gov/servlets/purl/1421620.
@article{osti_1421620,
title = {Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems},
author = {D'Elia, M. and Edwards, H. C. and Hu, J. and Phipps, E. and Rajamanickam, S.},
abstractNote = {Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of samplingbased uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble when applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated KarhunenLoève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.},
doi = {10.1137/16m1066324},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
number = 1,
volume = 6,
place = {United States},
year = {2018},
month = {1}
}