An Accurate and Stable Unsupervised Physics-Inspired Neural Network Method for 2-D Electromagnetic Inverse Scattering

An unsupervised deep learning framework is proposed for solving 2-D electromagnetic inverse scattering problems (ISPs) with either full- or phaseless-data (PD), featuring good accuracy, stability, and generalization. The proposed method first establishes a mapping based on the scattering-field integral equation (SFIE), where the scattering field data is the input of the neural network (NN), and the total electric field and the permittivity distribution are the outputs. Then, two residual terms derived from the SFIE and total-field integral equation (TFIE) are embedded into the loss function as physics-inspired constraints for nonlinear electromagnetic problems. Furthermore, Laplacian regularization and a ReLU-based soft constraint are incorporated to enhance the training stability of the network and improve the performance of inversion. Numerical and experimental results demonstrate that the proposed method achieves higher accuracy, stronger noise robustness, and better artifact suppression compared with traditional inversion techniques. Owing to the unsupervised nature, the proposed method exhibits excellent generalization ability without labeled data. These advantages indicate that the proposed approach provides a stable, accurate, and label-free solution to electromagnetic inverse scattering.