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dc.contributor.authorZerbinati, Umberto
dc.date.accessioned2022-12-01T07:55:06Z
dc.date.available2022-05-17T07:22:02Z
dc.date.available2022-10-20T12:31:54Z
dc.date.available2022-12-01T07:55:06Z
dc.date.issued2022-09-23
dc.identifier.citationZerbinati, U. (2022). PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems. IFAC-PapersOnLine, 55(20), 61–66. https://doi.org/10.1016/j.ifacol.2022.09.072
dc.identifier.issn2405-8963
dc.identifier.doi10.1016/j.ifacol.2022.09.072
dc.identifier.urihttp://hdl.handle.net/10754/677982
dc.description.abstractPhysics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differential equations, given the fact they escape the curse of dimensionality. In this paper, we present Physics Informed Neural Networks as an underdetermined point matching collocation method then expose the connection between Galerkin Least Squares (GALS) and PINNs, to develop an a priori error estimate, in the context of elliptic problems. In particular, techniques that belong to the realm of least squares finite elements and Rademacher complexity analysis are used to obtain the error estimate.
dc.description.sponsorshipI would like to express my deepest appreciation to Prof. G. Turkiyyah and Dr. S. Zampini without whom this paper would not have been possible.
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S2405896322012551
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [JournalTitle], [55, 20, (2022-09-23)] DOI: 10.1016/j.ifacol.2022.09.072 . © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectMachine Learning
dc.subjectLeast -squares method
dc.subjectFinite Element Analysis
dc.subjectPhysics Informed Neural Networks
dc.subjectA Priori Error Estimate
dc.titlePINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems
dc.typeConference Paper
dc.contributor.departmentKing Abdullah University Of Science and Technology, Thuwal, SA
dc.conference.date2022-07-27 to 2022-07-29
dc.conference.name10th Vienna International Conference on Mathematical Modelling, MATHMOD 2022
dc.conference.locationVienna, AUT
dc.identifier.wosutWOS:000860842100011
dc.eprint.versionPublisher's Version/PDF
dc.identifier.volume55
dc.identifier.issue20
dc.identifier.pages61-66
pubs.publication-statusPublished
dc.identifier.arxivid2202.01059
kaust.personZerbinati, Umberto R.
dc.identifier.eid2-s2.0-85142214184
refterms.dateFOA2022-05-17T07:22:45Z


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NOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [JournalTitle], [55, 20, (2022-09-23)] DOI: 10.1016/j.ifacol.2022.09.072 . © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Except where otherwise noted, this item's license is described as NOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [JournalTitle], [55, 20, (2022-09-23)] DOI: 10.1016/j.ifacol.2022.09.072 . © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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