Incorporating Local Hölder Regularity into PINNs for Solving Elliptic PDEs
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918179034365952 |
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| author | Zhou, Qirui Sun, Jiebao Ran, Yi Wu, Boying |
| author_facet | Zhou, Qirui Sun, Jiebao Ran, Yi Wu, Boying |
| contents | In this paper, local Hölder regularization is incorporated into a physics-informed neural networks (PINNs) framework for solving elliptic partial differential equations (PDEs). Motivated by the interior regularity properties of linear elliptic PDEs, a modified loss function is constructed by introducing local Hölder regularization term. To approximate this term effectively, a variable-distance discrete sampling strategy is developed. Error estimates are established to assess the generalization performance of the proposed method. Numerical experiments on a range of elliptic problems demonstrate notable improvements in both prediction accuracy and robustness compared to standard physics-informed neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incorporating Local Hölder Regularity into PINNs for Solving Elliptic PDEs Zhou, Qirui Sun, Jiebao Ran, Yi Wu, Boying Numerical Analysis In this paper, local Hölder regularization is incorporated into a physics-informed neural networks (PINNs) framework for solving elliptic partial differential equations (PDEs). Motivated by the interior regularity properties of linear elliptic PDEs, a modified loss function is constructed by introducing local Hölder regularization term. To approximate this term effectively, a variable-distance discrete sampling strategy is developed. Error estimates are established to assess the generalization performance of the proposed method. Numerical experiments on a range of elliptic problems demonstrate notable improvements in both prediction accuracy and robustness compared to standard physics-informed neural networks. |
| title | Incorporating Local Hölder Regularity into PINNs for Solving Elliptic PDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.26365 |