Physics-Informed neural networks with transfer learning for space charge impedances in particle accelerators

The physics-informed neural network (PINN) method, which is a powerful approach for solving partial differential equations with deep learning, has been recently applied to modeling of electrodynamic interaction problems including a relativistic beam in charged particle accelerators. In the present study, the transfer learning (TL) is applied to the PINN based on the total-field (TF) formulation. It is shown that TL can accelerate significantly the training process of the TF-PINN in the simulation of the space charge impedances of an infinitely long beam pipe of elliptical and rectangular cross section.