Error Estimates for Deep Learning Methods in Fluid Dynamics

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dc.contributor.authorBiswas, Animikh
dc.contributor.authorTian, Jing
dc.contributor.authorUlusoy, Suleyman
dc.date.accessioned2020-09-11T16:46:59Z
dc.date.available2020-09-11T16:46:59Z
dc.date.issued2022-05-31
dc.description.abstractIn this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier–Stokes equations. In particular, we obtain explicit error estimates (in suitable norms) for the solution computed by optimizing a loss function in a Deep Neural Network approximation of the solution, with a fixed complexity.en_US
dc.description.sponsorshipJ. Tian’s work is supported in part by the AMS Simons Travel Grant and the Jess and Mildred Fisher Endowed Professor fund of Mathematics from the Fisher College of Science and Mathematics at Towson University.en_US
dc.description.urihttps://link.springer.com/article/10.1007/s00211-022-01294-zen_US
dc.format.extent25 pagesen_US
dc.genrejournal articlesen_US
dc.identifierdoi:10.13016/m2o6jj-vw4n
dc.identifier.citationBiswas, A., Tian, J. & Ulusoy, S. Error estimates for deep learning methods in fluid dynamics. Numer. Math. 151, 753–777 (2022). https://doi.org/10.1007/s00211-022-01294-zen_US
dc.identifier.urihttps://doi.org/10.1007/s00211-022-01294-z
dc.language.isoen_USen_US
dc.publisherSpringer
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis is a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
dc.rightsPublic Domain Mark 1.0
dc.rightshttps://creativecommons.org/publicdomain/mark/1.0/
dc.titleError Estimates for Deep Learning Methods in Fluid Dynamicsen_US
dc.typeTexten_US
dcterms.creatorhttps://orcid.org/0000-0001-8594-0568

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