Coordinate-Residual Physics-Driven Neural Network for Electromagnetic Inverse Scattering

Electromagnetic inverse scattering is a nonlinear and ill-posed problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. The proposed solver directly reconstructs the unknown contrast distribution using normalized spatial coordinates and a residual convolutional network, without requiring a preliminary reconstruction. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10\%, compared with 7.97\% for CSI and 3.99\% for $L_{2/3}$-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Supplementary 2-D comparisons further confirm its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications. The related code is available at https://github.com/Physics-driven-methods.

Fast Physics-Driven Untrained Network for Highly Nonlinear Inverse Scattering Problems

Untrained neural networks (UNNs) offer high-fidelity electromagnetic inverse scattering reconstruction but are computationally limited by high-dimensional spatial-domain optimization. We propose a Real-Time Physics-Driven Fourier-Spectral (PDF) solver that achieves sub-second reconstruction through spectral-domain dimensionality reduction. By expanding induced currents using a truncated Fourier basis, the optimization is confined to a compact low-frequency parameter space supported by scattering measurements. The solver integrates a contraction integral equation (CIE) to mitigate high-contrast nonlinearity and a contrast-compensated operator (CCO) to correct spectral-induced attenuation. Furthermore, a bridge-suppressing loss is formulated to enhance boundary sharpness between adjacent scatterers. Numerical and experimental results demonstrate a 100-fold speedup over state-of-the-art UNNs with robust performance under noise and antenna uncertainties, enabling real-time microwave imaging applications.

Improved Physics-Driven Neural Network to Solve Inverse Scattering Problems

This paper presents an improved physics-driven neural network (IPDNN) framework for solving electromagnetic inverse scattering problems (ISPs). A new Gaussian-localized oscillation-suppressing window (GLOW) activation function is introduced to stabilize convergence and enable a lightweight yet accurate network architecture. A dynamic scatter subregion identification strategy is further developed to adaptively refine the computational domain, preventing missed detections and reducing computational cost. Moreover, transfer learning is incorporated to extend the solver's applicability to practical scenarios, integrating the physical interpretability of iterative algorithms with the real-time inference capability of neural networks. Numerical simulations and experimental results demonstrate that the proposed solver achieves superior reconstruction accuracy, robustness, and efficiency compared with existing state-of-the-art methods.