Physics-Informed Neural Networks for the Numerical Modeling of Steady-State and Transient Electromagnetic Problems with Discontinuous Media
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.04380
- arXiv:
- arXiv:2406.04380
- Bibcode:
- 2024arXiv240604380N
- Keywords:
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- Physics - Computational Physics
- E-Print:
- 3 dimensional and transient problems with discontinuous media