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

Abstract

Abstract 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.