Parametric and Uncertainty Computations with Tensor Product Representations

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.
Type de document :
Communication dans un congrès
Andrew M. Dienstfrey; Ronald F. Boisvert. 10th Working Conference on Uncertainty Quantification in Scientific Computing (WoCoUQ), Aug 2011, Boulder, CO, United States. Springer, IFIP Advances in Information and Communication Technology, AICT-377, pp.139-150, 2012, Uncertainty Quantification in Scientific Computing. 〈10.1007/978-3-642-32677-6_9〉
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01518676
Contributeur : Hal Ifip <>
Soumis le : vendredi 5 mai 2017 - 10:55:58
Dernière modification le : vendredi 5 mai 2017 - 10:57:09
Document(s) archivé(s) le : dimanche 6 août 2017 - 12:39:28

Fichier

978-3-642-32677-6_9_Chapter.pd...
Fichiers produits par l'(les) auteur(s)

Licence


Distributed under a Creative Commons Paternité 4.0 International License

Identifiants

Citation

Hermann Matthies, Alexander Litvinenko, Oliver Pajonk, Bojana Rosić, Elmar Zander. Parametric and Uncertainty Computations with Tensor Product Representations. Andrew M. Dienstfrey; Ronald F. Boisvert. 10th Working Conference on Uncertainty Quantification in Scientific Computing (WoCoUQ), Aug 2011, Boulder, CO, United States. Springer, IFIP Advances in Information and Communication Technology, AICT-377, pp.139-150, 2012, Uncertainty Quantification in Scientific Computing. 〈10.1007/978-3-642-32677-6_9〉. 〈hal-01518676〉

Partager

Métriques

Consultations de la notice

150

Téléchargements de fichiers

60