Inverse Electromagnetic Scattering for Doubly-Connected Cylinders using Convolutional Neural Networks

TL;DR

This work tackles inverse electromagnetic scattering for a magneto-dielectric cylinder coated by an impedance boundary by framing it as a two-step divide-and-conquer problem: first classify the obstacle shape, then perform class-specific reconstruction of the boundary and impedance. A novel end-to-end 1D multi-channel circular-padding CNN processes angular far-field measurements, preserving $2\pi$ periodicity and exploiting cross-channel correlations to estimate both geometry and impedance. Training data are generated via a boundary integral formulation of the direct problem, enabling robust supervision for classification and regression across peanut-, kite-, and star-shaped obstacles, including scenarios with fixed or variable impedance and added measurement noise. The results demonstrate high classification accuracy and very strong regression performance for simpler shapes, with increased data and model capacity required for the more complex star-shaped geometries; misclassifications near decision boundaries still yield reliable reconstructions. The approach offers a data-driven, non-invasive alternative to classical boundary integral methods and highlights avenues for extending to non-constant impedance and richer material parameterization, with publicly shareable code to follow.

Abstract

In this work, we consider the inverse electromagnetic scattering problem for a magneto-dielectric cylinder covering an impedance cylinder of arbitrary shape. We solve it by introducing a divide-and-conquer framework using specially designed 1D multi-channel, circular-padding Convolutional Neural Networks. The solution of the direct problem provides us with the real and imaginary components of the far-field measurements representing the input data. We first classify the shape of the impedance cylinder and then reconstruct the unknown boundary curve and the impedance function. Through extensive numerical experiments, including noisy scenarios, we demonstrate the efficiency and robustness of our approach.

Figures (28)

• Figure 1: Electromagnetic scattering by a doubly-connected magneto-dielectric cylinder. 3D (left) and cross-section (right).
• Figure 2: Representative example of the ill-posedness of the inverse problem: two different star-shaped obstacles (left) produce nearly identical far-field data (right).
• Figure 3: Architecture of the circular padding CNN and MLP inversion head, forming an end‐to‐end network from raw input measurements to final outputs.
• Figure 4: Illustration of a sliding window of length $K^{(1)}=5$ moving along the $T_0=128$ angular measurement positions of the $C_0=4$ input channels.
• Figure 5: Element‐wise convolution for a single filter: a $5\times 4$ kernel multiplies a 5-angle, 4-channel patch.