GT-04 Kolmogorov-Arnold Network for 2-D Magnetostatic Fields Solving
Creators: Yachao Zhu
Kai Xu
Bingkuan Wan
Gang Lei and Jianguo Zhu
Publisher: name: IEEE
Year: 2025

The data-driven machine-learning approach has significantly advanced the development of computational electromagnetics. Numerous research highlight the successful utility of magnetic materials and field modelling or prediction. Most current studies present multilayer perception (MLP) leveraged physics-informed neural network (PINN) to integrate empirical data and available physical prior knowledge into the machine learning process. However, the MLP-based PINN may face intensive computation resource limitations from its fixed activation function, particularly in large-scale fitting tasks [1]. This study introduces the development and application of Kolmogorov-Arnold Networks (KAN) as a novel method to overcome these limitations. Unlike MLP-PINN, KAN uses the learnable activation functions associated with network edges and eliminates linear weights. Univariate functions parameterized by B-spline have been employed to construct the activation function in KAN's architecture [2]. This study presents two illustrative examples of solving magnetostatic field problems grounded in electromagnetic theory. It established the partial differential equation (PDE) of the magnetic vector potential A expression under a given current density. The analysis includes the magnetic vector potential A in two geometrical settings: square and circular regions. The KAN is compared with finite difference methods (FDM) and MLP-PINN, which approve of its performance while magnetostatic field fitting. The results indicate that the KANs can achieve higher accuracy with less computational overhead when predicting magnetic potentials. The following Fig.1 states the fitting result of KAN and disturbing error with FDM. Fig. 2 shows the MLP-PINN required more epochs than KAN, which reached the same training loss level.References: [1] H. Wang, L. Lu, S. Song and G. Huang, Communications in Computational Physics., Vol. 34, p. 869-906 (2023) [2] Z. Liu et al., arXiv preprint., arXiv:2404.19756 (2024)
The data-driven machine-learning approach has significantly advanced the development of computational electromagnetics. Numerous research highlight the successful utility of magnetic materials and field modelling or prediction. Most current studies present multilayer perception (MLP) leveraged physics-informed neural network (PINN) to integrate empirical data and available physical prior knowledge into the machine learning process. However, the MLP-based PINN may face intensive computation resource limitations from its fixed activation function, particularly in large-scale fitting tasks [1]. This study introduces the development and application of Kolmogorov-Arnold Networks (KAN) as a novel method to overcome these limitations. Unlike MLP-PINN, KAN uses the learnable activation functions associated with network edges and eliminates linear weights. Univariate functions parameterized by B-spline have been employed to construct the activation function in KAN's architecture [2]. This study presents two illustrative examples of solving magnetostatic field problems grounded in electromagnetic theory. It established the partial differential equation (PDE) of the magnetic vector potential A expression under a given current density. The analysis includes the magnetic vector potential A in two geometrical settings: square and circular regions. The KAN is compared with finite difference methods (FDM) and MLP-PINN, which approve of its performance while magnetostatic field fitting. The results indicate that the KANs can achieve higher accuracy with less computational overhead when predicting magnetic potentials. The following Fig.1 states the fitting result of KAN and disturbing error with FDM. Fig. 2 shows the MLP-PINN required more epochs than KAN, which reached the same training loss level.References: [1] H. Wang, L. Lu, S. Song and G. Huang, Communications in Computational Physics., Vol. 34, p. 869-906 (2023) [2] Z. Liu et al., arXiv preprint., arXiv:2404.19756 (2024)