Self-Adaptive Physics-Informed Neural Networks for Solving 2-D Magnetostatic Fields in Open Boundaries

Open-boundary 2-D magnetostatic field problems are computationally challenging for traditional numerical methods. This work proposes MagOpenNet, a physics-informed neural network (PINN) framework that introduces the concept of the 1-D and 2-D Astley Infinite Element Method (IEM), along with a self-adaptive weighting strategy, to address the complexities of predictions for both interior and exterior domains. Benchmark tests on circular geometry show that MagOpenNet attains at least 73.2 % reduction compared to the Finite Element Method (FEM) in computation time, 15.58 % reduction compared to IEM and 73.42 % reduction compared to the Finite Difference Method (FDM), with an average of 98.6 % accuracy. The transfer learning-based bus duct, C-core, and U-core benchmarks yield a similar outcome. Compared to traditional PINNs, MagOpenNet achieves up to 36.61 % time reduction in training. These results demonstrate that MagOpenNet provides an alternative for high computational efficiency, high accuracy, strong generalisation ability and stable convergence for open boundary magnetostatic analyses.