Physics-Informed Neural Networks Based on Unsupervised Learning for Multidomain Electromagnetic Analysis

Physics-informed neural networks (PINNs) have attracted much attention recently due to their unique advantages, such as directly fitting the strong form of partial differential equations (PDEs) and not requiring a mesh. These advantages make them suitable for solving numerical analysis problems of complex three-dimensional shapes. Since supervised-learning-based PINNs rely on the solutions obtained from traditional numerical methods, they should be regarded as performing function fitting or numerical approximation rather than truly solving a numerical computation problem. On the other hand, PINNs based on unsupervised learning can successfully solve single-domain electromagnetic analysis problems without access to the value of the physical quantity, which can be considered the ground truth. However, they cannot solve the multidomain electromagnetic analysis problem because they cannot fit the physical quantity at the interface. If the solution at the interface is unknown, PINNs can only enforce the continuity of values at the interface. Still, they cannot express the relationship between the gradients at the interface. To address this problem, this research proposes a novel numerical analysis method that employs PINNs based on unsupervised learning to solve multidomain problems. The discretised direct boundary integral equations are utilised to solve the physical quantity at the interface, and the multidomain problem can be transformed into multiple single-domain problems. Then, PINNs based on unsupervised learning can be utilised to solve all the subdomains. The feasibility of the proposed method is demonstrated through single-domain and multidomain electrostatic box problems as well as the testing electromagnetic analysis methods (TEAM) problem 22. Finally, the results of finite element analysis (FEA), boundary element method (BEM) and PINN based on unsupervised learning are compared, and the accuracy of the proposed method is proved. The FEM and analytical solutions of TEAM problem 22 are compared and discussed to confirm the accuracy of the presented numerical method.