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 1.8dB over the best competing method on real Fresnel data.
This paper proposes a level-set-based physics-driven neural network solver (LSPDNN) for 3-D electromagnetic inverse scattering. To mitigate boundary blurring and reconstruction artifacts in voxel-wise contrast reconstruction, the proposed solver exploits the piecewise homogeneity of practical scatterers by representing unknown targets with multiple coordinate-dependent neural level-set components. Specifically, a soft-union multi-material model is proposed to separately describe the object support and material distribution. The global support is formed by the union of multiple level-set components, while the local contrast is determined by normalized component weights and learnable complex permittivity candidates. In addition, a model-consistent total variation (TV) regularization is imposed on the material-region indicators, rather than directly on the reconstructed contrast, to suppress fragmented material assignments without excessively smoothing material interfaces. An adaptive loss balancing strategy is further introduced to reduce the dependence on manually selected regularization weights. For each measurement instance, the neural level-set parameters and material candidates are optimized by minimizing a physics-consistent objective function. Numerical and experimental results demonstrate that LSPDNN can reconstruct scatterers with clear boundaries, more uniform material regions, and substantially reduced background artifacts. The results highlight the advantage of the neural level-set parameterization in challenging 3-D inverse scattering cases involving irregular shapes, closely spaced objects, multiple materials, and measurement noise.
Electromagnetic inverse scattering is a nonlinear and ill-posed computational imaging 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. CRPDNN represents the unknown complex contrast distribution using normalized spatial coordinates and a residual convolutional network, whose parameters are optimized by enforcing consistency between the measured and model-predicted scattered fields. Unlike existing subregion-accelerated PDNN approaches, CRPDNN does not require a preliminary reconstruction, thereby avoiding dependence on its accuracy. 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 L2/3-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Additional 2-D comparisons further demonstrate 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.
Reconstructing continuous physical fields from sparse measurements is a central inverse problem, but data-driven generative models can produce states that violate governing dynamics. We introduce a physics-informed generative solver that separates stable prior learning from inference-time enforcement of conservation laws. Martingale-Regularized Score Matching regularizes score pretraining with a Score Fokker-Planck constraint, yielding a dynamically stable prior. Physics-Informed Implicit Score Sampling then guides denoising trajectories by gradients of physical residuals, projecting samples toward admissible manifolds without retraining. In acoustics, the method co-generates pressure and particle velocity from sparse sensors, enabling dense virtual arrays that suppress spatial aliasing. The same framework generalizes to real-world ERA5 meteorological fields under extreme sparsity. Together, this work establishes a rigorous and generalizable paradigm for solving high-dimensional inverse problems, bridging the gap between generative artificial intelligence and first-principles science.