Physics-Guided Residual Learning for Full-Angular-Domain Scattering Prediction of Coding Metasurfaces

Coding metasurfaces provide an effective approach for manipulating electromagnetic scattering through discrete coding states. However, obtaining angular-domain scattering responses for a large number of coding configurations remains computationally expensive with full-wave electromagnetic simulations. To address this issue, this work proposes a Physics-Guided Residual Learning (PGRL) framework for rapid radar cross section (RCS) prediction over the full angular domain. A discrete-aperture model provides an approximate physics-based scattering prior, and a residual convolutional neural network learns the discrepancy between this prior and the full-wave reference in the dBsm domain. Periodic azimuthal encoding, angular-gradient features, and validity information are incorporated into the input representation. Furthermore, a structure-preserving loss jointly constrains pointwise RCS values, angular gradients, and local curvature. Experiments are conducted on a finite 16 × 16 1-bit coding metasurface at 9 GHz under normal incidence and x-polarized excitation. PGRL achieves an RMSE of 3.67 dB, an MAE of 2.74 dB, and a mean coefficient of determination of 0.86, with improved overall prediction performance compared with the considered baselines. Ablation experiments further evaluate the contributions of the physics-aware representation, training objective and regularization, periodic azimuthal encoding, and baseline-gradient features under controlled settings. These results demonstrate the effectiveness of combining an approximate physics-based scattering prior with data-driven residual correction for the investigated electromagnetic setting. Application to other structures, operating conditions, or experimental measurement data remains subject to model adaptation and independent validation.