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.

中文翻译：

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DAL-PINNs：基于达朗贝尔原理的物理信息神经网络，用于广义电磁场模型计算


物理信息神经网络（PINN）已被广泛用作偏微分方程（PDE）的求解器，并在物理场模拟领域被广泛引用。然而，与传统的数值方法相比，PINN 在训练精度方面并没有表现出显着的优势。此外，电磁场计算涉及各种控制方程，需要构建特定的PINN损失函数进行训练，这限制了它们在计算电磁学中的适用性。为了解决这些问题，本文提出了一种多场景电磁场计算的通用算法，称为 DAL-PINN。通过将麦克斯韦方程组重新表述为具有可变参数的通用偏微分方程，只需调整源和材料参数即可解决不同的电磁场问题。基于达朗贝尔原理和定点采样，通过用随机变量（虚拟位移）代替插值函数，对算法进行了有效改进。通过静态、扩散和波动场景下的电磁场计算验证了所提出算法的性能。