Beyond Data-Physics Consistency: A Cross-Correlated Physics-Informed Neural Network for Robust Inverse Scattering

The electromagnetic inverse scattering problem (ISP), due to its inherent strong nonlinearity and severe ill-posedness, has long been a core challenge in microwave imaging. In recent years, physics-informed neural networks (PINNs) have provided a novel paradigm for solving ISPs by embedding Maxwell's equations into the deep learning optimization process. However, conventional PINN methods rely solely on independent data-equation and state-equation residuals to construct the consistency loss, which easily causes them to fall into local minima and suffer from low computational efficiency when facing high-contrast targets or multi-frequency observation data. To transcend the traditional data-physics consistency framework, this paper proposes a novel cross-correlated physics-informed neural network (CC-PINN). The core innovations of this work include: (1) constructing a Fourier feature MLP network architecture based on weight normalization, which possesses excellent capability for solving inverse scattering problems; (2) introducing a cross-correlated residual term that directly couples the reconstructed dielectric parameters and the predicted internal total field to the external observation field, breaking the decoupling between the contrast source and the permittivity optimization in traditional PINNs and significantly enhancing the robustness of PINNs for ISP; (3) introducing a zero-padding-based 2D-FFT acceleration algorithm, which reduces the computational complexity of the forward Green's function integration. Experimental results on synthetic and measured data demonstrate that CC-PINN can reconstruct high-contrast dielectric targets with high fidelity, and its convergence robustness far exceeds that of PINN algorithms using classical cost functions, regardless of whether simultaneous multi-frequency processing or frequency-hopping strategies are employed.