Electromagnetic Field Reconstruction and Source Identification Using Conditional Variational Autoencoder and CNN

In this work, a Deep Learning approach based on a Conditional Variational Autoencoder (CVAE) and a Convolutional Neural Network (CNN) has been adopted for the solution of inverse problems and electromagnetic field reconstruction; the method is applied to the TEAM 35 benchmark magnetostatic problem. The aim of the proposed method is twofold: first, knowing the magnetic field distribution in a subdomain, the magnetic field distribution ${\bm{B}}$ in the whole domain is determined (field reconstruction problem). For this problem a CVAE is proposed and trained. The CVAE prediction is based on an optimization procedure in the latent space, which uses an automatic differentiation technique. Subsequently, knowing the magnetic field distribution in the whole domain, the aim is to find, using a CNN regression model, the geometrical characteristics of the source (source identification problem).