An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems
Recently, one artificial intelligence technique, known as artificial neural network (ANN), has brought advanced development to the arena of mathematical research. It competes effectively with other traditional methods in providing accurate solutions for fractional differential equations (FDEs). This...
| Main Authors: | , , , |
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| Format: | Article |
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Springer Nature
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/113731/ |
| _version_ | 1848866305998848000 |
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| author | Admon, Mohd Rashid Senu, Norazak Ahmadian, Ali Abdul Majid, Zanariah |
| author_facet | Admon, Mohd Rashid Senu, Norazak Ahmadian, Ali Abdul Majid, Zanariah |
| author_sort | Admon, Mohd Rashid |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Recently, one artificial intelligence technique, known as artificial neural network (ANN), has brought advanced development to the arena of mathematical research. It competes effectively with other traditional methods in providing accurate solutions for fractional differential equations (FDEs). This work aims to implement a feedforward ANN with two hidden layers to solve nonlinear systems based on the fractional Riccati differential equation (FRDE). The network parameters are trained using the Adam optimization method with the aid of automatic differentiation. A vectorization algorithm is designated for the selected step to make the computation process more efficient. Two different initial value problems in integer-order derivatives and fractional-order derivatives are discussed. Numerical results demonstrate that the proposed method not only closely matches the exact solutions and reference solutions but also is more accurate than other existing methods. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. |
| first_indexed | 2025-11-15T14:18:30Z |
| format | Article |
| id | upm-113731 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:18:30Z |
| publishDate | 2024 |
| publisher | Springer Nature |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1137312025-01-15T07:56:07Z http://psasir.upm.edu.my/id/eprint/113731/ An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems Admon, Mohd Rashid Senu, Norazak Ahmadian, Ali Abdul Majid, Zanariah Recently, one artificial intelligence technique, known as artificial neural network (ANN), has brought advanced development to the arena of mathematical research. It competes effectively with other traditional methods in providing accurate solutions for fractional differential equations (FDEs). This work aims to implement a feedforward ANN with two hidden layers to solve nonlinear systems based on the fractional Riccati differential equation (FRDE). The network parameters are trained using the Adam optimization method with the aid of automatic differentiation. A vectorization algorithm is designated for the selected step to make the computation process more efficient. Two different initial value problems in integer-order derivatives and fractional-order derivatives are discussed. Numerical results demonstrate that the proposed method not only closely matches the exact solutions and reference solutions but also is more accurate than other existing methods. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024. Springer Nature 2024 Article PeerReviewed Admon, Mohd Rashid and Senu, Norazak and Ahmadian, Ali and Abdul Majid, Zanariah (2024) An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems. Computational and Applied Mathematics, 43 (6). art. no. 362. ISSN 2238-3603; eISSN: 1807-0302 https://link.springer.com/article/10.1007/s40314-024-02865-6?error=cookies_not_supported&code=0cf46fe4-c73d-4503-babd-00f86730c80d 10.1007/s40314-024-02865-6 |
| spellingShingle | Admon, Mohd Rashid Senu, Norazak Ahmadian, Ali Abdul Majid, Zanariah An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems |
| title | An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems |
| title_full | An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems |
| title_fullStr | An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems |
| title_full_unstemmed | An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems |
| title_short | An advanced scheme based on Artificial Intelligence technique for solving nonlinear Riccati systems |
| title_sort | advanced scheme based on artificial intelligence technique for solving nonlinear riccati systems |
| url | http://psasir.upm.edu.my/id/eprint/113731/ http://psasir.upm.edu.my/id/eprint/113731/ http://psasir.upm.edu.my/id/eprint/113731/ |