Physics-Informed Neural Network Approaches for 2D Magnetic Field Modeling in Cartesian Coordinates: Residual-Based and Energy-Based Training Strategies

Yıldız H., Poyraz Koçak Y., Uzal E.

6th INTERNATIONAL CONGRESS OF ENGINEERING AND NATURAL SCIENCES STUDIES, Ankara, Türkiye, 4 - 05 Haziran 2026, ss.408-423, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.408-423
  • İstanbul Üniversitesi-Cerrahpaşa Adresli: Evet

Özet

Physics-Informed Neural Networks (PINNs) have become an alternative approach for solving partial differential equations without requiring traditional mesh-based numerical methods. In this study, a PINN-based framework is proposed for modeling the two-dimensional magnetic field distribution generated by a coil in the Cartesian coordinate system using Maxwell’s equations. The study focuses on a region containing a coil in order to investigate the learning performance of PINNs under electromagnetic conditions. Two different training strategies are investigated within the same PINN framework. In the first, the loss function is constructed using the residuals of the governing differential equation and boundary conditions. In the second approach, a variational energy-based formulation is used by minimizing the magnetic energy functional of the system. The performances of both methods are comparatively analyzed in terms of convergence behavior, training stability, and smoothness of the obtained magnetic field distribution. In addition, the magnetic field distribution obtained from the PINN models is compared with results computed using the Finite Difference Analysis (FDA) method. Numerical results demonstrate that both PINN approaches can successfully approximate the magnetic vector potential and magnetic field distribution in the coil domain with results consistent with FDA solutions. However, the variational energy-based approach provides more stable convergence and smoother field representations during training. The study highlights the applicability of physics-informed deep learning methods for computational electromagnetics and presents a comparison between residual-based and energy-based PINN optimization strategies.