Academic Journal
Hybrid PINN-IFE approach for solving transmission problems in circular interface domains.
| Τίτλος: | Hybrid PINN-IFE approach for solving transmission problems in circular interface domains. |
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| Συγγραφείς: | Azam, Muhammad, Alhwikem, Dalal, Ullah, Naseer |
| Πηγή: | AIMS Mathematics; 2026, Vol. 11 Issue 4, p1-31, 31p |
| Θεματικοί όροι: | Helmholtz equation, Finite element method, Numerical analysis, Theory of wave motion, Boundary value problems, Computational physics |
| Περίληψη: | In this study, we proposed a hybrid methodology combining Physics-Informed Neural Networks (PINNs) and Immersed Finite Element (IFE) methods to address transmission problems in complex geometries, with a focus on Helmholtz-type equations. The technique addressed the challenge of solving wave equations in domains with circular interfaces, where material properties differ across the interface. The hybrid model leverages the strengths of PINNs to enforce the governing physical equations and IFE to provide a coarse initial solution, which is then corrected by the neural network using a signed-distance function to the interface. This correction was trained on a combination of supervised loss from data, physics-informed residual predictions, and interface conditions. Numerical experiments demonstrated high precision of the proposed technique when compared with manufactured exact solutions, achieving low error levels in both subdomains. High-frequency tests at ω = 100 further validated the method's accuracy and robustness across material configurations including normal and inverted contrast cases. Its mesh-free character provides flexibility and versatility for a wide range of transmission problems in computational physics, making it a promising method for solving interface-related issues in wave propagation. [ABSTRACT FROM AUTHOR] |
| Copyright of AIMS Mathematics is the property of American Institute of Mathematical Sciences 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.) | |
| Βάση Δεδομένων: | Complementary Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Hybrid PINN-IFE approach for solving transmission problems in circular interface domains. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Azam%2C+Muhammad%22">Azam, Muhammad</searchLink><br /><searchLink fieldCode="AR" term="%22Alhwikem%2C+Dalal%22">Alhwikem, Dalal</searchLink><br /><searchLink fieldCode="AR" term="%22Ullah%2C+Naseer%22">Ullah, Naseer</searchLink> – Name: TitleSource Label: Source Group: Src Data: AIMS Mathematics; 2026, Vol. 11 Issue 4, p1-31, 31p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Theory+of+wave+motion%22">Theory of wave motion</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+physics%22">Computational physics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this study, we proposed a hybrid methodology combining Physics-Informed Neural Networks (PINNs) and Immersed Finite Element (IFE) methods to address transmission problems in complex geometries, with a focus on Helmholtz-type equations. The technique addressed the challenge of solving wave equations in domains with circular interfaces, where material properties differ across the interface. The hybrid model leverages the strengths of PINNs to enforce the governing physical equations and IFE to provide a coarse initial solution, which is then corrected by the neural network using a signed-distance function to the interface. This correction was trained on a combination of supervised loss from data, physics-informed residual predictions, and interface conditions. Numerical experiments demonstrated high precision of the proposed technique when compared with manufactured exact solutions, achieving low error levels in both subdomains. High-frequency tests at ω = 100 further validated the method's accuracy and robustness across material configurations including normal and inverted contrast cases. Its mesh-free character provides flexibility and versatility for a wide range of transmission problems in computational physics, making it a promising method for solving interface-related issues in wave propagation. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of AIMS Mathematics is the property of American Institute of Mathematical Sciences 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 1 Subjects: – SubjectFull: Helmholtz equation Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Theory of wave motion Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Computational physics Type: general Titles: – TitleFull: Hybrid PINN-IFE approach for solving transmission problems in circular interface domains. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Azam, Muhammad – PersonEntity: Name: NameFull: Alhwikem, Dalal – PersonEntity: Name: NameFull: Ullah, Naseer IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 24736988 Numbering: – Type: volume Value: 11 – Type: issue Value: 4 Titles: – TitleFull: AIMS Mathematics Type: main |
| ResultId | 1 |