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

Journal Article · · SIAM/ASA Journal on Uncertainty Quantification
DOI:https://doi.org/10.1137/17M1141096· OSTI ID:1459932
 [1];  [1];  [1];  [1];  [1];  [1];  [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
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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.

Research Organization:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
DARPA; USDOE
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1459932
Alternate ID(s):
OSTI ID: 1510845
OSTI ID: 1478334
Report Number(s):
SAND2018-6855J; 664904
Journal Information:
SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 2 Vol. 6; ISSN 2166-2525
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (1)

A new surrogate modeling method combining polynomial chaos expansion and Gaussian kernel in a sparse Bayesian learning framework journal July 2019

Figures / Tables (24)

Table 1(p. 6)table Table 1
Algorithm 1(p. 7)figure Algorithm 1
Figure 1(p. 10)figure Figure 1
Figure 2(p. 11)figure Figure 2
Figure 3(p. 12)figure Figure 3
Figure 4(p. 13)figure Figure 4
Figure 5(p. 14)figure Figure 5
Figure 6(p. 14)figure Figure 6
Figure 7(p. 16)figure Figure 7
Figure 8(p. 17)figure Figure 8
Figure 10(p. 18)figure Figure 10
Figure 9(p. 18)figure Figure 9
Table 2(p. 19)table Table 2
Figure 11(p. 20)figure Figure 11
Figure 12(p. 21)figure Figure 12
Figure 13(p. 22)figure Figure 13
Table 3(p. 22)table Table 3
Figure 14(p. 23)figure Figure 14
Table 4(p. 23)table Table 4
Table 5(p. 23)table Table 5
Figure 15(p. 24)figure Figure 15
Table 6(p. 24)table Table 6
Figure 16(p. 25)figure Figure 16
Table 7(p. 25)table Table 7

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