Physics-Informed Neural Networks with Data and Equation Scaling for Time Domain Electromagnetic Fields

Abstract

Solving partial differential equations with deep learning techniques is recently discussed in an emerging field of scientific computing combined with machine learning methodologies. The physics-informed neural networks (PINNs) is one of the promising approaches in this context. By using data and equation scaling, two different PINNs for an electromagnetic initial-boundary value problem with extremely different scales of space and time are constructed and verified in comparison with the exact solution. We clarify that both PINNs can be used as surrogates to the time domain solution of an electromagnetic wave problem for a closed empty cavity with perfectly electric conductor walls.