Physics-Informed Radial Basis Function Neural Networks for two-dimensional magnetostatic field modeling
PHYSICA SCRIPTA, cilt.101, sa.44, ss.446005-446036, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 101 Sayı: 44
- Basım Tarihi: 2026
- Doi Numarası: 10.1088/1402-4896/aeb8cf
- Dergi Adı: PHYSICA SCRIPTA
- Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), Chemical Abstracts Core, Compendex, INSPEC, zbMATH
- Sayfa Sayıları: ss.446005-446036
- İstanbul Üniversitesi-Cerrahpaşa Adresli: Evet
Özet
Magnetic field modeling is essential for a wide range of applications, from electromagnetic device design to the analysis of geomagnetic and material-based systems. This study proposes two distinct neural network frameworks based on physics-informed radial basis function neural networks (PI-RBFNNs) to solve Maxwell’s equations on four different domains. The proposed unified and domain-specific network architectures use region-aware radial basis function kernels and are initialized by collocation governing equations in boundary and jump conditions. The models capture magnetic field behavior in both homogeneous and heterogeneous regions, with the level of agreement depending on the problem complexity and network architecture. All models are implemented using the TensorFlow framework, which enables efficient automatic differentiation and scalable optimization. Unlike conventional mesh-based numerical methods, the proposed PI-RBFNN framework provides a mesh-free formulation for magnetostatic field modeling. To evaluate the effectiveness of the models, results obtained from both configurations are compared with benchmark data from the literature and solutions generated by the finite difference method (FDM). The results show good agreement for simpler configurations, while discrepancies increase for more heterogeneous problems. For intermediate cases, the domain-specific architecture reduces the relative L2 error with respect to FDM compared with the unified architecture. These findings demonstrate the potential of PI-RBFNN architectures for mesh-free modeling of magnetostatic field problems involving heterogeneous material regions and interface conditions, while further validation against independently converged reference solutions is required for broader assessment of their accuracy.