A Deep Learning Scheme of Electromagnetic Scattering From Scatterers With Incomplete Profiles

TL;DR

This work tackles EM forward/inverse scattering when a scatterer's profile is only partially known, by formulating forward scattering for incompletely known targets and solving the coupled forward–inverse problem with a DL-based scheme. The method employs two neural networks to estimate the missing profile $\bm{\chi}^{p2}$ and the total field increment $\Delta \mathbf{E}^{tot}$ using the known portion $\bm{\chi}^{p1}$ and limited data $\mathbf{E}^{sca}_0$, grounded in operator representations $\mathcal{L}_{\chi}$ and $\mathcal{L}_E$. Validation on 2-D and 3-D dielectric scatterers, including MNIST/EMNIST shapes and metasurfaces, shows accurate reconstruction (low MRE) and fast predictions compared with conventional solvers, with robust generalization across incident directions, contrasts, and geometries. The approach demonstrates that DL can compensate for incomplete profiles and enable reliable scattering predictions in realistic sensing and imaging scenarios, highlighting practical potential for rapid EM characterization using limited measurements.

Abstract

A deep learning scheme is proposed to solve the electromagnetic (EM) scattering problems where the profile of the dielectric scatterer of interest is incomplete. As a compensation, a limited amount of scattering data is provided, which is in principle containing sufficient information associated with the missing part of the profile. The existing solvers can hardly realize the compensation if the known part of the profile and the scattering data are combined straightforwardly. On one hand, the well-developed forward solvers have no mechanism to accept the scattering data, which can recover the unknown part of the profile if properly used. On the other hand, the existing solvers for inverse problems cannot retrieve the complete profile with an acceptable accuracy from the limited amount of scattering data, even when the available part of the profile can be fed into the solvers. This work aims to handle the difficulty. To this end, the EM forward scattering from an incompletely known dielectric scatterer is derived. A scheme based on DL is then proposed where the forward and inverse scattering problems are solved simultaneously. Numerical experiments are conducted to demonstrate the performance of the proposed DL-based scheme for both two-dimensional (2-D) and three-dimensional (3-D) EM scattering problems.

Figures (17)

• Figure 1: Configuration of the forward/inverse scattering problem
• Figure 2: An example of incomplete profile of a scatterer.
• Figure 3: The overflow of the developed DL-based learning scheme. $\oplus$ means to put the matrices on both sides of the symbol into the two channels of the tensor. $\Re(\cdot)$ and $\Im(\cdot)$ denote to take the real and imaginary part of the corresponding tensor, respectively.
• Figure 4: The sketch of the employed 3-D U-Net.
• Figure 5: Examples of samples contained in the MNIST training set. The first and second columns show the real part of the complete and incomplete profiles, respectively. The third and forth columns present the imaginary part of the complete and incomplete profiles, respectively.