Revising recurrent neural networks to eliminate numerical derivatives in forming Physics-Informed loss terms with respect to time.
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| Title: | Revising recurrent neural networks to eliminate numerical derivatives in forming Physics-Informed loss terms with respect to time. |
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| Authors: | Jahani-nasab, Mahyar1 (AUTHOR), Bijarchi, Mohamad Ali1 (AUTHOR) bijarchi@sharif.edu |
| Source: | Computational Mechanics. Apr2026, Vol. 77 Issue 4, p867-884. 18p. |
| Subjects: | Recurrent neural networks, Numerical differentiation, Back propagation, Partial differential equations, Time, Inverse problems |
| Abstract: | Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the complexities of numerical derivatives into the training process of these models. In this study, we propose modifying the structure of the traditional RNN to enable the prediction of each block over a time interval, making it possible to calculate the derivative of the output with respect to time using the backpropagation algorithm. To achieve this, the time intervals of these blocks are overlapped, defining a mutual loss function between them. Additionally, the employment of conditional hidden states enables us to achieve a unique solution for each block. The forget factor is utilized to control the influence of the conditional hidden state on the prediction of the subsequent block. This novel architecture, termed the Mutual Interval RNN (MI-RNN), excels in extrapolation, long-term temporal simulation, and inverse parameter discovery tasks. The MI-RNN exhibits lower loss values during training and superior extrapolation accuracy compared to vanilla physics-informed neural network (PINN) architectures. [ABSTRACT FROM AUTHOR] |
| Copyright of Computational 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193283572 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Revising recurrent neural networks to eliminate numerical derivatives in forming Physics-Informed loss terms with respect to time. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jahani-nasab%2C+Mahyar%22">Jahani-nasab, Mahyar</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Bijarchi%2C+Mohamad+Ali%22">Bijarchi, Mohamad Ali</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bijarchi@sharif.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Apr2026, Vol. 77 Issue 4, p867-884. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Recurrent+neural+networks%22">Recurrent neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+differentiation%22">Numerical differentiation</searchLink><br /><searchLink fieldCode="DE" term="%22Back+propagation%22">Back propagation</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Time%22">Time</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the complexities of numerical derivatives into the training process of these models. In this study, we propose modifying the structure of the traditional RNN to enable the prediction of each block over a time interval, making it possible to calculate the derivative of the output with respect to time using the backpropagation algorithm. To achieve this, the time intervals of these blocks are overlapped, defining a mutual loss function between them. Additionally, the employment of conditional hidden states enables us to achieve a unique solution for each block. The forget factor is utilized to control the influence of the conditional hidden state on the prediction of the subsequent block. This novel architecture, termed the Mutual Interval RNN (MI-RNN), excels in extrapolation, long-term temporal simulation, and inverse parameter discovery tasks. The MI-RNN exhibits lower loss values during training and superior extrapolation accuracy compared to vanilla physics-informed neural network (PINN) architectures. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computational 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/s00466-025-02691-5 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 867 Subjects: – SubjectFull: Recurrent neural networks Type: general – SubjectFull: Numerical differentiation Type: general – SubjectFull: Back propagation Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Time Type: general – SubjectFull: Inverse problems Type: general Titles: – TitleFull: Revising recurrent neural networks to eliminate numerical derivatives in forming Physics-Informed loss terms with respect to time. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jahani-nasab, Mahyar – PersonEntity: Name: NameFull: Bijarchi, Mohamad Ali IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01787675 Numbering: – Type: volume Value: 77 – Type: issue Value: 4 Titles: – TitleFull: Computational Mechanics Type: main |
| ResultId | 1 |
