Physics-Informed Neural Networks for Studying Charge Dynamics in Air

Paper in proceeding, 2023

To establish a theoretical background for designing high voltage gas insulated systems, it is important to understand the charge dynamics under high electrical stress in air and other gases. Models used today for describing discharges and charge transport in gases related to discharges are comprised of partial different equations that are typically solved by numerical methods such as the finite element method (FEM). Such simulations are often tedious and have several shortcomings such as convergence problems, low accuracy due to numerical diffusion, etc. Recently, a new method called Physics-Informed Neural Networks (PINN) has been proposed which uses differential equations as constraints for training neural networks in such a way that a proper approximation to the solutions can be found. In the present work we explore how PINN can be used to solve some differential equations that are critical to studies of discharges and charge dynamics in gases. One very encouraging finding is that PINN solutions for charge density distributions with steep gradients do not show any numerical diffusion and instabilities that is in strong contrast to solutions with FEM.