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This content will become publicly available on June 19, 2019

Title: Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

Here, compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several compressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers l1_ls, SpaRSA, CGIST, FPC_AS, and ADMM, we develop techniques to mitigate overfitting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendations on parameter settings for these techniques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-crossflow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy, and computational trade-offs between polynomial bases of different degrees, and practicability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.
Authors:
ORCiD logo [1] ;  [1] ;  [1] ;  [1] ;  [1] ;  [1] ;  [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Report Number(s):
SAND-2018-6855J
Journal ID: ISSN 2166-2525; 664904
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
SIAM/ASA Journal on Uncertainty Quantification
Additional Journal Information:
Journal Volume: 6; Journal Issue: 2; Journal ID: ISSN 2166-2525
Publisher:
SIAM
Research Org:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org:
Defense Advanced Research Projects Agency (DARPA); USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; uncertainty quantification; LASSO; compressed sensing; sparse regression; sparse reconstruction; sequential compressive sensing
OSTI Identifier:
1459932