Regularization-Augmented Physics-Informed Neural Networks for Electromagnetic Inverse Scattering

Abstract

This paper proposes a regularization-augmented physics-informed neural network (RAPINN) framework based on the volume integral equation (VIE) for electromagnetic inverse scattering problems. By incorporating the VIE, the scattered field is evaluated through the Green’s function, allowing the neural networks to reconstruct the total field only inside the domain of interest and reducing the computational burden for far-field problems. To avoid repeated forward solves, the inverse problem is reformulated as an optimal-control-inspired physics-constrained optimization problem. For each inverse problem, a complex-valued field module and a real-valued contrast module are jointly optimized through the data-equation and state-equation residuals, replacing explicit matrix inversion with residual-based optimization. The resulting vanilla PINN framework achieves accuracy comparable to NN-based inversion with lower computational cost. To improve robustness in challenging cases, squared total-variation-like (squared TV) smoothness regularization and Tikhonov regularization are further incorporated into the PINN loss to form RAPINN. By introducing prior information on the scatterer, these explicit regularization terms complement the implicit constraints imposed by the physics residuals and help mitigate unstable reconstructions produced by the vanilla PINN in high-contrast and noisy scenarios. Numerical results show that RAPINN provides more stable and accurate reconstructions than conventional methods and vanilla PINN in the tested cases.