A Physics-Constrained Neural Network for Electromagnetic Inverse Scattering Imaging

To accurately and robustly solve electromagnetic inverse scattering problems, a physics-constrained neural network (PCNN) method is proposed in this work. The method adopts Born iteration framework, where a neural network is embedded in each iteration to solve the optimization problem. It combines the linearization capability of traditional inverse methods with the powerful capability of neural networks in solving complex optimization tasks. In the neural network, theL2norm of data equation is adopted as the loss function. Since the data equation directly corresponds to the target inverse problem, it provides an effective physical constraint that guides the network toward the correct solution. Furthermore, a constraint layer is incorporated in the network to restrict the solution within predefined physical bounds, thereby narrowing the feasible solution space and improving inversion stability. The synthetic and experimental results show that the proposed PCNN method consistently achieves lower RMSE and data error and higher SSIM than conventional BIM, PINN-based methods and U-Net-based supervised learning approaches, demonstrating its superior accuracy in reconstruction. These results confirm that the PCNN offers an effective and robust unsupervised learningbased approach for nonlinear electromagnetic inverse scattering problems.