Parametric and uncertainty computations with tensor product representations

Hermann G. Matthies*, Alexander Litvinenko, Oliver Pajonk, Bojana V. Rosić, Elmar Zander

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

14 Citations (Scopus)

Abstract

Computational uncertainty quantification in a probabilistic setting is a special case of a parametric problem. Parameter dependent state vectors lead via association to a linear operator to analogues of covariance, its spectral decomposition, and the associated Karhunen-Loève expansion. From this one obtains a generalised tensor representation The parameter in question may be a tuple of numbers, a function, a stochastic process, or a random tensor field. The tensor factorisation may be cascaded, leading to tensors of higher degree. When carried on a discretised level, such factorisations in the form of low-rank approximations lead to very sparse representations of the high dimensional quantities involved. Updating of uncertainty for new information is an important part of uncertainty quantification. Formulated in terms or random variables instead of measures, the Bayesian update is a projection and allows the use of the tensor factorisations also in this case.

Original languageEnglish
Title of host publicationUncertainty Quantification in Scientific Computing
Subtitle of host publication10th IFIP WG 2.5 Working Conference, WoCoUQ 2011, Revised Selected Papers
EditorsAndrew M. Dienstfrey, Ronald F. Boisvert
Place of PublicationBerlin, Heidelberg
PublisherSpringer
Pages139-150
Number of pages12
ISBN (Electronic)978-3-642-32677-6
ISBN (Print)978-3-642-32676-9
DOIs
Publication statusPublished - 1 Jan 2012
Externally publishedYes
Event10th IFIP WG 2.5 Working Conference on Uncertainty Quantification in Scientific Computing, WoCoUQ 2011 - Boulder, United States
Duration: 1 Aug 20114 Aug 2011
Conference number: 10

Publication series

NameIFIP Advances in Information and Communication Technology
PublisherSpringer
Volume377
ISSN (Print)1868-4238
ISSN (Electronic)1861-2288

Conference

Conference10th IFIP WG 2.5 Working Conference on Uncertainty Quantification in Scientific Computing, WoCoUQ 2011
Abbreviated titleWoCoUQ
CountryUnited States
CityBoulder
Period1/08/114/08/11

Keywords

  • Bayesian updating
  • low-rank tensor approximation
  • parametric problems
  • uncertainty quantification

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