Academic Journal
A physics-informed deep learning approach for solving strongly degenerate parabolic problems.
| Title: | A physics-informed deep learning approach for solving strongly degenerate parabolic problems. |
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| Authors: | Ambrosio, Pasquale, Cuomo, Salvatore, De Rosa, Mariapia |
| Source: | Engineering with Computers; Dec2025, Vol. 41 Issue 6, p4013-4029, 17p |
| Abstract: | In recent years, Scientific Machine Learning (SciML) methods for solving Partial Differential Equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving initial-boundary value problems involving nonlinear PDEs. Recently, PINNs have shown promising results in several application fields. Motivated by applications to gas filtration problems, here we present and evaluate a PINN-based approach to predict solutions to strongly degenerate parabolic problems with asymptotic structure of Laplacian type. To the best of our knowledge, this is one of the first papers demonstrating the efficacy of the PINN framework for solving such kind of problems. In particular, we estimate an appropriate approximation error for some test problems whose analytical solutions are fortunately known. The numerical experiments discussed include two and three-dimensional spatial domains, emphasizing the effectiveness of this approach in predicting accurate solutions. [ABSTRACT FROM AUTHOR] |
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| Database: | Complementary Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://dx.doi.org/doi:10.1007/s00366-024-01961-9 Name: EDS - Springer Nature Journals (s7799221) Category: fullText Text: View record at Springer |
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| Items | – Name: Title Label: Title Group: Ti Data: A physics-informed deep learning approach for solving strongly degenerate parabolic problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Ambrosio%2C+Pasquale%22">Ambrosio, Pasquale</searchLink><br /><searchLink fieldCode="AR" term="%22Cuomo%2C+Salvatore%22">Cuomo, Salvatore</searchLink><br /><searchLink fieldCode="AR" term="%22De+Rosa%2C+Mariapia%22">De Rosa, Mariapia</searchLink> – Name: TitleSource Label: Source Group: Src Data: Engineering with Computers; Dec2025, Vol. 41 Issue 6, p4013-4029, 17p – Name: Abstract Label: Abstract Group: Ab Data: In recent years, Scientific Machine Learning (SciML) methods for solving Partial Differential Equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving initial-boundary value problems involving nonlinear PDEs. Recently, PINNs have shown promising results in several application fields. Motivated by applications to gas filtration problems, here we present and evaluate a PINN-based approach to predict solutions to strongly degenerate parabolic problems with asymptotic structure of Laplacian type. To the best of our knowledge, this is one of the first papers demonstrating the efficacy of the PINN framework for solving such kind of problems. In particular, we estimate an appropriate approximation error for some test problems whose analytical solutions are fortunately known. The numerical experiments discussed include two and three-dimensional spatial domains, emphasizing the effectiveness of this approach in predicting accurate solutions. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Engineering with Computers 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/s00366-024-01961-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 4013 Titles: – TitleFull: A physics-informed deep learning approach for solving strongly degenerate parabolic problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ambrosio, Pasquale – PersonEntity: Name: NameFull: Cuomo, Salvatore – PersonEntity: Name: NameFull: De Rosa, Mariapia IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 01770667 Numbering: – Type: volume Value: 41 – Type: issue Value: 6 Titles: – TitleFull: Engineering with Computers Type: main |
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