Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 367, Issue -, Pages 49-64Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.04.026
Keywords
Polynomial chaos expansions; Uncertainty quantification; Compressive sampling; Gradient-enhanced l(1)-minimization
Funding
- NSFC [11671265]
- Program for Outstanding Academic leaders in Shanghai City [151503100]
- AFOSR [FA9550-15-1-0467]
- DARPA [N660011524053]
- National Natural Science Foundation of China [91630312, 91630203, 11571351, 11688101, 11731006]
- science challenge project, NCMIS [TZ2018001]
- youth innovation promotion association (CAS)
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We investigate a gradient enhanced l(1)-minimization for constructing sparse polynomial chaos expansions. In addition to function evaluations, measurements of the function gradient is also included to accelerate the identification of expansion coefficients. By designing appropriate preconditioners to the measurement matrix, we show gradient enhanced l(1) minimization leads to stable and accurate coefficient recovery. The framework for designing preconditioners is quite general and it applies to recover of functions whose domain is bounded or unbounded. Comparisons between the gradient enhanced approach and the standard l(1)-minimization are also presented and numerical examples suggest that the inclusion of derivative information can guarantee sparse recovery at a reduced computational cost. (c) 2018 Elsevier Inc. All rights reserved.
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