A Novel Hybrid Boundary Element—Physics Informed Neural Network Method for Numerical Solutions in Electromagnetics

Abstract

In this contribution the authors propose a hybrid Boundary Element Method – Physics Informed Neural Networks (BEM – PINN) approach, to be used for the resolution of partial differential equations arising when formulating boundary-value problems in electromagnetism. The approach retains both the advantages of integral methods (compact representation and no need to mesh large domains) and differential methods, where the term “differential” refers here to the Automatic Differentiation carried out during the training phase of the PINN. The method is easy to implement and adds an additional flexibility to purely PINN based solution methods.

Keywords

• Boundary element method
• physics informed neural networks
• Laplace equation