DAL-PINNs: Physics-informed neural networks based on D'Alembert principle for generalized electromagnetic field model computation

Abstract

Physics-Informed Neural Networks (PINNs) have been extensively used as solvers for partial differential equations (PDEs) and have been widely referenced in the field of physical field simulations. However, compared to traditional numerical methods, PINNs do not demonstrate significant advantages in terms of training accuracy. In addition, electromagnetic field computation involves various governing equations, which necessitate the construction of specific PINN loss functions for training, which limits their applicability in computational electromagnetics. To address these issues, this paper proposes a general algorithm for multi-scenario electromagnetic field calculation called DAL-PINN. By reformulating Maxwell's equations into a general PDE with variable parameters, different electromagnetic field problems can be solved by simply adjusting the source and material parameters. Based on D'Alembert's principle and fixed-point sampling, the algorithm is effectively improved by replacing interpolation functions with random variables (virtual displacements). The performance of the proposed algorithm is validated through the electromagnetic field calculation in static, diffusion, and wave scenarios.