Physics-Informed Neural Networks for the Numerical Modeling of Steady-State and Transient Electromagnetic Problems with Discontinuous Media
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910475480989696 |
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| author | Nohra, Michel Dufour, Steven |
| author_facet | Nohra, Michel Dufour, Steven |
| contents | Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize three-dimensional electromagnetic, parametric problems, with material discontinuities, covering both static and transient regimes. By replacing the discontinuous material properties with a continuous approximation, we eliminate the need to directly enforce interface conditions. Using the Neural Tangent Kernel (NTK) analysis, we show that using the first-order formulation of Maxwell's equations is more suitable for interface problems. We introduce a PINN-based decomposition on overlapping domains to enhance the convergence rate of the PINN. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Neural Networks for the Numerical Modeling of Steady-State and Transient Electromagnetic Problems with Discontinuous Media Nohra, Michel Dufour, Steven Computational Physics Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize three-dimensional electromagnetic, parametric problems, with material discontinuities, covering both static and transient regimes. By replacing the discontinuous material properties with a continuous approximation, we eliminate the need to directly enforce interface conditions. Using the Neural Tangent Kernel (NTK) analysis, we show that using the first-order formulation of Maxwell's equations is more suitable for interface problems. We introduce a PINN-based decomposition on overlapping domains to enhance the convergence rate of the PINN. |
| title | Physics-Informed Neural Networks for the Numerical Modeling of Steady-State and Transient Electromagnetic Problems with Discontinuous Media |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2406.04380 |