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.

ScoreField: Neural Inverse Scattering with Score-Based Generative Priors

Designing an effective electromagnetic inverse-scattering solver requires faithful enforcement of nonlinear full-wave physics together with an expressive prior on the unknown permittivity contrast. We propose ScoreField, a neural inverse scattering framework that integrates coupled implicit neural representations (INRs) with a pretrained score-based generative prior. ScoreField employs two INRs to parameterize the permittivity contrast and the induced current fields, and jointly optimize them under the Lippmann-Schwinger equations. In addition to the implicit regularization by the INR architecture, the score model provides a learned prior gradient on the contrast, which is propagated to the contrast INR through the chain rule. This formulation enables ScoreField to effectively handle strong multiple scattering, where nonlinear wave interactions require accurate modeling of the coupled full-wave physics. We evaluate ScoreField on simulated weak- and strong-scattering benchmarks, the canonical Austria phantom, and experimental Fresnel measurements. We note that ScoreField significantly improves reconstruction fidelity and suppresses artifacts relative to classical full-wave methods and deep learning baselines, achieving an average PSNR improvement of $1.8 \, \mathrm{dB}$ over the best competing method on real Fresnel data.