Conformal mapping based Physics-informed neural networks for designing neutral inclusions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914299963768832 |
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| author | Cho, Daehee Yun, Hyeonmin Lee, Jaeyong Lim, Mikyoung |
| author_facet | Cho, Daehee Yun, Hyeonmin Lee, Jaeyong Lim, Mikyoung |
| contents | We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse problem, leading to the development of Conformal Mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrate geometric function theory with PINNs. CoCo-PINNs effectively solve forward-inverse problems by modeling the interface function through neural network training, which yields a neutral inclusion effect. This approach enhances the performance of PINNs in terms of credibility, consistency, and stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal mapping based Physics-informed neural networks for designing neutral inclusions Cho, Daehee Yun, Hyeonmin Lee, Jaeyong Lim, Mikyoung Machine Learning Artificial Intelligence Analysis of PDEs We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse problem, leading to the development of Conformal Mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrate geometric function theory with PINNs. CoCo-PINNs effectively solve forward-inverse problems by modeling the interface function through neural network training, which yields a neutral inclusion effect. This approach enhances the performance of PINNs in terms of credibility, consistency, and stability. |
| title | Conformal mapping based Physics-informed neural networks for designing neutral inclusions |
| topic | Machine Learning Artificial Intelligence Analysis of PDEs |
| url | https://arxiv.org/abs/2501.07809 |