skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Limited-memory adaptive snapshot selection for proper orthogonal decomposition

Abstract

Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance 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 time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass 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 decomposition-based 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:
 [1];  [1];  [1];  [1]
  1. 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):
LLNL-TR-669265
DOE Contract Number:  
AC52-07NA27344
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., Kostova-Vassilevska, Tanya, Arrighi, Bill, and Chand, Kyle. Limited-memory adaptive snapshot selection for proper orthogonal decomposition. United States: N. p., 2015. Web. doi:10.2172/1224940.
Oxberry, Geoffrey M., Kostova-Vassilevska, Tanya, Arrighi, Bill, & Chand, Kyle. Limited-memory adaptive snapshot selection for proper orthogonal decomposition. United States. doi:10.2172/1224940.
Oxberry, Geoffrey M., Kostova-Vassilevska, Tanya, Arrighi, Bill, and Chand, Kyle. Thu . "Limited-memory adaptive snapshot selection for proper orthogonal decomposition". United States. doi:10.2172/1224940. https://www.osti.gov/servlets/purl/1224940.
@article{osti_1224940,
title = {Limited-memory adaptive snapshot selection for proper orthogonal decomposition},
author = {Oxberry, Geoffrey M. and Kostova-Vassilevska, Tanya and Arrighi, Bill and Chand, Kyle},
abstractNote = {Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance 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 time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass 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 decomposition-based 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}
}

Technical Report:

Save / Share: