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dc.contributor.authorKutyniok, Gitta Astrid Hildegard
dc.contributor.authorPetersen, Philipp
dc.contributor.authorRaslan, Mones
dc.contributor.authorSchneider, Reinhold
dc.date.accessioned2021-12-03T12:22:52Z
dc.date.available2021-12-03T12:22:52Z
dc.date.issued2021-06-02
dc.description.abstractWe derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low dimensionality of the solution manifold to obtain approximation rates which are significantly superior to those provided by classical neural network approximation results. Concretely, we use the existence of a small reduced basis to construct, for a large variety of parametric partial differential equations, neural networks that yield approximations of the parametric solution maps in such a way that the sizes of these networks essentially only depend on the size of the reduced basis.en_US
dc.identifier.citationKutyniok, Petersen, Raslan, Schneider. A Theoretical Analysis of Deep Neural Networks and Parametric PDEs. Constructive approximation. 2021en_US
dc.identifier.cristinIDFRIDAID 1925797
dc.identifier.doi10.1007/s00365-021-09551-4
dc.identifier.issn0176-4276
dc.identifier.issn1432-0940
dc.identifier.urihttps://hdl.handle.net/10037/23257
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.journalConstructive approximation
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2021 The Author(s)en_US
dc.subjectVDP::Mathematics and natural science: 400::Physics: 430en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Fysikk: 430en_US
dc.titleA Theoretical Analysis of Deep Neural Networks and Parametric PDEsen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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