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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2407.20833 |
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| _version_ | 1866914892903088128 |
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| author | Nohra, Michel Dufour, Steven |
| author_facet | Nohra, Michel Dufour, Steven |
| contents | Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and data-driven problems. However, they perform poorly on problems where the solution exhibits high frequencies, such as discontinuities or sharp gradients. In this work, we develop a PINN-based solver for modeling three-dimensional, transient and static, parametric electromagnetic problems in discontinuous media. We use the first-order Maxwell's equations to train the neural network. We use a level-set function to represent the interface with a continuous function, and to enrich the network's inputs with high-frequencies and interface information. Finally, we validate the proposed methodology on multiple 3D, parametric, static, and transient problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximating electromagnetic fields in discontinuous media using a single physics-informed neural network Nohra, Michel Dufour, Steven Computational Physics Mathematical Physics Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and data-driven problems. However, they perform poorly on problems where the solution exhibits high frequencies, such as discontinuities or sharp gradients. In this work, we develop a PINN-based solver for modeling three-dimensional, transient and static, parametric electromagnetic problems in discontinuous media. We use the first-order Maxwell's equations to train the neural network. We use a level-set function to represent the interface with a continuous function, and to enrich the network's inputs with high-frequencies and interface information. Finally, we validate the proposed methodology on multiple 3D, parametric, static, and transient problems. |
| title | Approximating electromagnetic fields in discontinuous media using a single physics-informed neural network |
| topic | Computational Physics Mathematical Physics |
| url | https://arxiv.org/abs/2407.20833 |