Limitedmemory adaptive snapshot selection for proper orthogonal decomposition
Abstract
Reduced order models are useful for accelerating simulations in manyquery contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floatingpoint operation costs in highperformance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive timestepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decompositionbased reduced order models, and memory usage is minimized by computing the singular value decomposition using a singlepass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decompositionbased reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1224940
 Report Number(s):
 LLNLTR669265
 DOE Contract Number:
 AC5207NA27344
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; proper orthogonal decomposition; reduced order model; snapshot; incremental singular value decomposition
Citation Formats
Oxberry, Geoffrey M., KostovaVassilevska, Tanya, Arrighi, Bill, and Chand, Kyle. Limitedmemory adaptive snapshot selection for proper orthogonal decomposition. United States: N. p., 2015.
Web. doi:10.2172/1224940.
Oxberry, Geoffrey M., KostovaVassilevska, Tanya, Arrighi, Bill, & Chand, Kyle. Limitedmemory adaptive snapshot selection for proper orthogonal decomposition. United States. doi:10.2172/1224940.
Oxberry, Geoffrey M., KostovaVassilevska, Tanya, Arrighi, Bill, and Chand, Kyle. Thu .
"Limitedmemory adaptive snapshot selection for proper orthogonal decomposition". United States. doi:10.2172/1224940. https://www.osti.gov/servlets/purl/1224940.
@article{osti_1224940,
title = {Limitedmemory adaptive snapshot selection for proper orthogonal decomposition},
author = {Oxberry, Geoffrey M. and KostovaVassilevska, Tanya and Arrighi, Bill and Chand, Kyle},
abstractNote = {Reduced order models are useful for accelerating simulations in manyquery contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floatingpoint operation costs in highperformance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive timestepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decompositionbased reduced order models, and memory usage is minimized by computing the singular value decomposition using a singlepass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decompositionbased reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.},
doi = {10.2172/1224940},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2015},
month = {4}
}