In recent years, artificial intelligence technologies have been widely applied across various fields, demonstrating significant potential, particularly in scientific computing. This paper proposes a neural network approach based on Fourier features to solve partial differential equations (PDEs) related to electromagnetic physical laws, starting from the general solution form of PDEs. By integrating Physics-Informed Neural Networks (PINNs) with automatic differentiation techniques, a loss function is constructed based on PDEs and known conditions. The effectiveness and accuracy of this method are evaluated through computational validation on three electromagnetic problems with varying degrees of complexity, differing in equation forms, domain setups, and boundary conditions. Cross-validation methods are employed to assess the feasibility and predictive performance of the proposed approach.

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Application of Physical Information Neural Network Based on Fourier Features in Electromagnetic Computing

  • Yuqiu Sun,
  • Wei Xv

摘要

In recent years, artificial intelligence technologies have been widely applied across various fields, demonstrating significant potential, particularly in scientific computing. This paper proposes a neural network approach based on Fourier features to solve partial differential equations (PDEs) related to electromagnetic physical laws, starting from the general solution form of PDEs. By integrating Physics-Informed Neural Networks (PINNs) with automatic differentiation techniques, a loss function is constructed based on PDEs and known conditions. The effectiveness and accuracy of this method are evaluated through computational validation on three electromagnetic problems with varying degrees of complexity, differing in equation forms, domain setups, and boundary conditions. Cross-validation methods are employed to assess the feasibility and predictive performance of the proposed approach.