Show simple item record

dc.contributor.authorNobile, Fabio
dc.date.accessioned2017-06-05T08:35:49Z
dc.date.available2017-06-05T08:35:49Z
dc.date.issued2015-01-07
dc.identifier.urihttp://hdl.handle.net/10754/624117
dc.description.abstractWe consider a general problem F(u, y) = 0 where u is the unknown solution, possibly Hilbert space valued, and y a set of uncertain parameters. We specifically address the situation in which the parameterto-solution map u(y) is smooth, however y could be very high (or even infinite) dimensional. In particular, we are interested in cases in which F is a differential operator, u a Hilbert space valued function and y a distributed, space and/or time varying, random field. We aim at reconstructing the parameter-to-solution map u(y) from random noise-free or noisy observations in random points by discrete least squares on polynomial spaces. The noise-free case is relevant whenever the technique is used to construct metamodels, based on polynomial expansions, for the output of computer experiments. In the case of PDEs with random parameters, the metamodel is then used to approximate statistics of the output quantity. We discuss the stability of discrete least squares on random points show convergence estimates both in expectation and probability. We also present possible strategies to select, either a-priori or by adaptive algorithms, sequences of approximating polynomial spaces that allow to reduce, and in some cases break, the curse of dimensionality
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/6e425ffc82e646dfa703ba13f65a02b21d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
dc.titleDiscrete least squares polynomial approximation with random evaluations - application to PDEs with Random parameters
dc.typePresentation
dc.conference.dateJanuary 6-9, 2015
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
dc.conference.locationKAUST
dc.contributor.institutionÉcole Polytechnique Fédérale de Lausanne
refterms.dateFOA2018-06-13T17:26:47Z


Files in this item

This item appears in the following Collection(s)

Show simple item record