PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems
| dc.contributor.author | Zerbinati, Umberto | |
| dc.date.accessioned | 2022-12-01T07:55:06Z | |
| dc.date.available | 2022-05-17T07:22:02Z | |
| dc.date.available | 2022-10-20T12:31:54Z | |
| dc.date.available | 2022-12-01T07:55:06Z | |
| dc.date.issued | 2022-09-23 | |
| dc.identifier.citation | Zerbinati, 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.issn | 2405-8963 | |
| dc.identifier.doi | 10.1016/j.ifacol.2022.09.072 | |
| dc.identifier.uri | http://hdl.handle.net/10754/677982 | |
| dc.description.abstract | Physics 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.sponsorship | I 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.publisher | Elsevier BV | |
| dc.relation.url | https://linkinghub.elsevier.com/retrieve/pii/S2405896322012551 | |
| dc.rights | 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/ | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Machine Learning | |
| dc.subject | Least -squares method | |
| dc.subject | Finite Element Analysis | |
| dc.subject | Physics Informed Neural Networks | |
| dc.subject | A Priori Error Estimate | |
| dc.title | PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems | |
| dc.type | Conference Paper | |
| dc.contributor.department | King Abdullah University Of Science and Technology, Thuwal, SA | |
| dc.conference.date | 2022-07-27 to 2022-07-29 | |
| dc.conference.name | 10th Vienna International Conference on Mathematical Modelling, MATHMOD 2022 | |
| dc.conference.location | Vienna, AUT | |
| dc.identifier.wosut | WOS:000860842100011 | |
| dc.eprint.version | Publisher's Version/PDF | |
| dc.identifier.volume | 55 | |
| dc.identifier.issue | 20 | |
| dc.identifier.pages | 61-66 | |
| pubs.publication-status | Published | |
| dc.identifier.arxivid | 2202.01059 | |
| kaust.person | Zerbinati, Umberto R. | |
| dc.identifier.eid | 2-s2.0-85142214184 | |
| refterms.dateFOA | 2022-05-17T07:22:45Z |
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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/