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A weighted -minimization approach for sparse polynomial chaos expansions
Open accessAbstract
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1l1-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weighted l1l1-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.
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Citations
Cites
An Introduction To Compressive Sampling
Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
Cited by
POLYNOMIAL-CHAOS-BASED KRIGING
Schobi, R., Sudret, B., & Wiart, J. (2015) · International Journal for Uncertainty Quantification · doi:10.1615/int.j.uncertaintyquantification.2015012467 · Cited by 398
Metadata
- Authors
- Peng, J., Hampton, J., & Doostan, A.
- Venue
- Journal of Computational Physics
- Publisher
- Elsevier BV
- Published
- 2014-06
- Volume
- 267
- Pages
- 92-111
- ISSN
- 0021-9991 (ISSN-L)
- OpenAlex
- W1980635834
- Cited by
- 183
- References
- 1
- FWCI
- 14.28
- Type
- journal article
- Language
- en
- Open access
- green
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- Peng, J., Hampton, J., & Doostan, A. (2014). A weighted -minimization approach for sparse polynomial chaos expansions. Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2014.02.024
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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