Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks
Conventional methods for solving inverse wave problems struggle with ill-posedness, significant computational demands, and discretization errors. In this study, we propose an innovative framework for solving inverse problems in wave equations by using deep learning techniques with spacetime radial b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/5/725 |
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| author | Chih-Yu Liu Cheng-Yu Ku Wei-Da Chen Ying-Fan Lin Jun-Hong Lin |
| author_facet | Chih-Yu Liu Cheng-Yu Ku Wei-Da Chen Ying-Fan Lin Jun-Hong Lin |
| author_sort | Chih-Yu Liu |
| collection | DOAJ |
| description | Conventional methods for solving inverse wave problems struggle with ill-posedness, significant computational demands, and discretization errors. In this study, we propose an innovative framework for solving inverse problems in wave equations by using deep learning techniques with spacetime radial basis functions (RBFs). The proposed method capitalizes on the pattern recognition strength of deep neural networks (DNNs) and the precision of spacetime RBFs in capturing spatiotemporal dynamics. By utilizing initial conditions, boundary data, and radial distances to construct spacetime RBFs, this approach circumvents the need for wave equation discretization. Notably, the model maintains accuracy even with incomplete or noisy boundary data, illustrating its robustness and offering significant advancements over traditional techniques in solving wave equations. |
| format | Article |
| id | doaj-art-9c33be4c8983461d836552aa63ca9c5c |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9c33be4c8983461d836552aa63ca9c5c2025-08-20T02:59:15ZengMDPI AGMathematics2227-73902025-02-0113572510.3390/math13050725Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural NetworksChih-Yu Liu0Cheng-Yu Ku1Wei-Da Chen2Ying-Fan Lin3Jun-Hong Lin4Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, TaiwanDepartment of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, TaiwanDepartment of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, TaiwanDepartment of Civil Engineering, Chung Yuan Christian University, Taoyuan 320314, TaiwanDepartment of Civil Engineering, Chung Yuan Christian University, Taoyuan 320314, TaiwanConventional methods for solving inverse wave problems struggle with ill-posedness, significant computational demands, and discretization errors. In this study, we propose an innovative framework for solving inverse problems in wave equations by using deep learning techniques with spacetime radial basis functions (RBFs). The proposed method capitalizes on the pattern recognition strength of deep neural networks (DNNs) and the precision of spacetime RBFs in capturing spatiotemporal dynamics. By utilizing initial conditions, boundary data, and radial distances to construct spacetime RBFs, this approach circumvents the need for wave equation discretization. Notably, the model maintains accuracy even with incomplete or noisy boundary data, illustrating its robustness and offering significant advancements over traditional techniques in solving wave equations.https://www.mdpi.com/2227-7390/13/5/725inverse problemswave equationsdeep learningphysics-informed neural networksradial basis functions |
| spellingShingle | Chih-Yu Liu Cheng-Yu Ku Wei-Da Chen Ying-Fan Lin Jun-Hong Lin Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks Mathematics inverse problems wave equations deep learning physics-informed neural networks radial basis functions |
| title | Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks |
| title_full | Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks |
| title_fullStr | Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks |
| title_full_unstemmed | Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks |
| title_short | Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks |
| title_sort | solving inverse wave problems using spacetime radial basis functions in neural networks |
| topic | inverse problems wave equations deep learning physics-informed neural networks radial basis functions |
| url | https://www.mdpi.com/2227-7390/13/5/725 |
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