Weak Formulation for Physics-Informed Neural Networks in the Resolution of Analysis Problems in Electromagnetics

A new class of neural networks has been recently introduced to solve problems based on some physical model. Such networks are called “Physical-Informed Neural Networks” (PINN). PINN are trained not based on input-output data, but rather by explicitly enforcing the model physical laws. More in detail, they are trained to minimize the “equations residual” in the physical model in each point of the domain rather than the discrepancy with known data. In this contribution, we propose to formulate the equations of ElectroMagnetism (EM) embedded in a PINN by using a weak formulation approach. This helps convergence of the training process, thanks to the lower derivation order required in the error computation. In addition, the presence of different materials in the domain is easily treated. In this digest, the approach is described in its fundamentals, and a simple example is presented.