Compressive Sampling Methods for Sparse Polynomial Chaos Expansions

Jerrad Hampton and Alireza Doostan ()
Additional contact information
Jerrad Hampton: University of Colorado, Aerospace Engineering Sciences
Alireza Doostan: University of Colorado, Aerospace Engineering Sciences

Chapter 24 in Handbook of Uncertainty Quantification, 2017, pp 827-855 from Springer

Abstract: Abstract A salient taskin uncertainty quantification (UQ) is to study the dependence of a quantity of interest (QoI) on input variables representing system uncertainties. Relying on linear expansions of the QoI in orthogonal polynomial bases of inputs, polynomial chaos expansions (PCEs) are now among the widely used methods in UQ. When there exists a smoothness in the solution being approximated, the PCE exhibits sparsity in that a small fraction of expansion coefficients are significant. By exploiting this sparsity, compressive sampling, also known as compressed sensing, provides a natural framework for accurate PCE using relatively few evaluations of the QoI and in a manner that does not require intrusion into legacy solvers. The PCE possesses a rich structure between the QoI being approximated, the polynomials, and input variables used to perform the approximation and where the QoI is evaluated. In this chapter insights are provided into this structure, summarizing a portion of the current literature on PCE via compressive sampling within the context of UQ.

Keywords: Legendre Polynomials; Hermite Polynomials; Orthogonal Polynomials; Compressed Sensing; Polynomial Chaos Expansions; Markov Chain Monte Carlo; ℓ 1-minimization; Basis Pursuit; Sparse Approximation (search for similar items in EconPapers)
Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12385-1_67

Ordering information: This item can be ordered from
http://www.springer.com/9783319123851

DOI: 10.1007/978-3-319-12385-1_67

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().