Exploring the inverse line-source scattering problem in dielectric cylinders with deep neural networks

This study presents a novel approach utilizing deep neural networks to address the inverse line-source scattering problem in dielectric cylinders. By employing Multi-layer Perceptron models, we intend to identify the number, positions, and strengths of hidden internal sources. This is performed by using single-frequency phased data, from limited measurements of real electric and real magnetic surface fields. Training data are generated by solving corresponding direct problems, using an exact solution representation. Through extended numerical experiments, we demonstrate the efficiency of our approach, including scenarios involving noise, reduced sample sizes, and fewer measurements. Additionally, we examine the empirical scaling laws governing model performance and conduct a local analysis to explore how our neural networks handle the inherent ill-posedness of the considered inverse problems.