Neural network solution based on the minimum potential energy principle for static problems of structural mechanics.
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| Title: | Neural network solution based on the minimum potential energy principle for static problems of structural mechanics. |
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| Authors: | Qian, Jiamin1 (AUTHOR), Chen, Lincong1 (AUTHOR), Sun, J. Q.2 (AUTHOR) jsun3@ucmerced.edu |
| Source: | Applied Mathematics & Mechanics. Jun2025, Vol. 46 Issue 6, p1125-1142. 18p. |
| Subjects: | Dirac function, Boundary value problems, Variational principles, Structural mechanics, Geographic boundaries |
| Abstract: | This paper presents the variational physics-informed neural network (VPINN) as an effective tool for static structural analyses. One key innovation includes the construction of the neural network solution as an admissible function of the boundary-value problem (BVP), which satisfies all geometrical boundary conditions. We then prove that the admissible neural network solution also satisfies natural boundary conditions, and therefore all boundary conditions, when the stationarity condition of the variational principle is met. Numerical examples are presented to show the advantages and effectiveness of the VPINN in comparison with the physics-informed neural network (PINN). Another contribution of the work is the introduction of Gaussian approximation of the Dirac delta function, which significantly enhances the ability of neural networks to handle singularities, as demonstrated by the examples with concentrated support conditions and loadings. It is hoped that these structural examples are so convincing that engineers would adopt the VPINN method in their structural design practice. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Neural network solution based on the minimum potential energy principle for static problems of structural mechanics. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Qian%2C+Jiamin%22">Qian, Jiamin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Lincong%22">Chen, Lincong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sun%2C+J%2E+Q%2E%22">Sun, J. Q.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jsun3@ucmerced.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Mechanics%22">Applied Mathematics & Mechanics</searchLink>. Jun2025, Vol. 46 Issue 6, p1125-1142. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Dirac+function%22">Dirac function</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+principles%22">Variational principles</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+mechanics%22">Structural mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Geographic+boundaries%22">Geographic boundaries</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents the variational physics-informed neural network (VPINN) as an effective tool for static structural analyses. One key innovation includes the construction of the neural network solution as an admissible function of the boundary-value problem (BVP), which satisfies all geometrical boundary conditions. We then prove that the admissible neural network solution also satisfies natural boundary conditions, and therefore all boundary conditions, when the stationarity condition of the variational principle is met. Numerical examples are presented to show the advantages and effectiveness of the VPINN in comparison with the physics-informed neural network (PINN). Another contribution of the work is the introduction of Gaussian approximation of the Dirac delta function, which significantly enhances the ability of neural networks to handle singularities, as demonstrated by the examples with concentrated support conditions and loadings. It is hoped that these structural examples are so convincing that engineers would adopt the VPINN method in their structural design practice. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10483-025-3257-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1125 Subjects: – SubjectFull: Dirac function Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Variational principles Type: general – SubjectFull: Structural mechanics Type: general – SubjectFull: Geographic boundaries Type: general Titles: – TitleFull: Neural network solution based on the minimum potential energy principle for static problems of structural mechanics. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Qian, Jiamin – PersonEntity: Name: NameFull: Chen, Lincong – PersonEntity: Name: NameFull: Sun, J. Q. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02534827 Numbering: – Type: volume Value: 46 – Type: issue Value: 6 Titles: – TitleFull: Applied Mathematics & Mechanics Type: main |
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