Enhancing sparsity of Hermite polynomial expansions by iterative rotations

Yang, Xiu; Lei, Huan; Baker, Nathan A.; Lin, Guang

doi:10.1016/j.jcp.2015.11.038

Title: Enhancing sparsity of Hermite polynomial expansions by iterative rotations

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Abstract

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.

Authors:

Yang, Xiu; Lei, Huan; Baker, Nathan A.;

Publication Date:: Mon Feb 01 00:00:00 EST 2016

Research Org.:: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1248437

Report Number(s):: PNNL-SA-110981
Journal ID: ISSN 0021-9991; KJ0401000

DOE Contract Number:: AC05-76RL01830

Resource Type:: Journal Article

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 307; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Citation Formats


                    Yang, Xiu, Lei, Huan, Baker, Nathan A., and Lin, Guang. Enhancing sparsity of Hermite polynomial expansions by iterative rotations.  United States: N. p., 2016. 
        Web.  doi:10.1016/j.jcp.2015.11.038.

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                    Yang, Xiu, Lei, Huan, Baker, Nathan A., & Lin, Guang. Enhancing sparsity of Hermite polynomial expansions by iterative rotations.  United States.  https://doi.org/10.1016/j.jcp.2015.11.038

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                    Yang, Xiu, Lei, Huan, Baker, Nathan A., and Lin, Guang. 2016.  
        "Enhancing sparsity of Hermite polynomial expansions by iterative rotations".  United States.  https://doi.org/10.1016/j.jcp.2015.11.038.

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@article{osti_1248437,

  title        = {Enhancing sparsity of Hermite polynomial expansions by iterative rotations},

  author       = {Yang, Xiu and Lei, Huan and Baker, Nathan A. and Lin, Guang},

  abstractNote = {Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation- based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O(100)) problems.},

  doi          = {10.1016/j.jcp.2015.11.038},

  url          = {https://www.osti.gov/biblio/1248437},
  journal      = {Journal of Computational Physics},

  issn         = {0021-9991},

  number       = ,

  volume       = 307,

  place        = {United States},

  year         = {Mon Feb 01 00:00:00 EST 2016},

  month        = {Mon Feb 01 00:00:00 EST 2016}

}

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https://doi.org/10.1016/j.jcp.2015.11.038

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