Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations
This paper introduces a novel multilayer neural network technique to solve partial differential equations with non-integer derivatives (FPDEs). The proposed model is a deep feed-forward multiple layer neural network (DFMLNN) that is trained using advanced optimization approaches, namely adaptive mom...
| Main Authors: | , , |
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| Format: | Article |
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John Wiley and Sons
2025
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| Online Access: | http://psasir.upm.edu.my/id/eprint/120691/ |
| _version_ | 1848868218167361536 |
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| author | Ali, Amina Hassan Senu, Norazak Ahmadian, Ali |
| author_facet | Ali, Amina Hassan Senu, Norazak Ahmadian, Ali |
| author_sort | Ali, Amina Hassan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper introduces a novel multilayer neural network technique to solve partial differential equations with non-integer derivatives (FPDEs). The proposed model is a deep feed-forward multiple layer neural network (DFMLNN) that is trained using advanced optimization approaches, namely adaptive moment estimation (Adam) and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), which integrate neural networks. First, the Adam method is employed for training, and then the model is further improved using L-BFGS. The Laplace transform is used, concentrating on the Caputo fractional derivative, to approximate the FPDE. The efficacy of this strategy is confirmed through rigorous testing, which involves making predictions and comparing the outcomes with exact solutions. The results illustrate that this combined approach greatly improves both precision and effectiveness. This proposed multilayer neural network offers a robust and reliable framework for solving FPDEs. |
| first_indexed | 2025-11-15T14:48:54Z |
| format | Article |
| id | upm-120691 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:48:54Z |
| publishDate | 2025 |
| publisher | John Wiley and Sons |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1206912025-10-08T06:19:18Z http://psasir.upm.edu.my/id/eprint/120691/ Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations Ali, Amina Hassan Senu, Norazak Ahmadian, Ali This paper introduces a novel multilayer neural network technique to solve partial differential equations with non-integer derivatives (FPDEs). The proposed model is a deep feed-forward multiple layer neural network (DFMLNN) that is trained using advanced optimization approaches, namely adaptive moment estimation (Adam) and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), which integrate neural networks. First, the Adam method is employed for training, and then the model is further improved using L-BFGS. The Laplace transform is used, concentrating on the Caputo fractional derivative, to approximate the FPDE. The efficacy of this strategy is confirmed through rigorous testing, which involves making predictions and comparing the outcomes with exact solutions. The results illustrate that this combined approach greatly improves both precision and effectiveness. This proposed multilayer neural network offers a robust and reliable framework for solving FPDEs. John Wiley and Sons 2025 Article PeerReviewed Ali, Amina Hassan and Senu, Norazak and Ahmadian, Ali (2025) Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 38 (4). art. no. e70073. ISSN 0894-3370; eISSN: 1099-1204 https://onlinelibrary.wiley.com/doi/10.1002/jnm.70073 10.1002/jnm.70073 |
| spellingShingle | Ali, Amina Hassan Senu, Norazak Ahmadian, Ali Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| title | Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| title_full | Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| title_fullStr | Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| title_full_unstemmed | Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| title_short | Multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| title_sort | multilayer neural networks enhanced with hybrid methods for solving fractional partial differential equations |
| url | http://psasir.upm.edu.my/id/eprint/120691/ http://psasir.upm.edu.my/id/eprint/120691/ http://psasir.upm.edu.my/id/eprint/120691/ |