Two-Stage Deformable-Convolutional Inverse Design of Nanophotonic Absorbers from Optical Spectra

Data-driven inverse design enables efficient generation of nanophotonic structures with prescribed optical responses, but spectrum-to-geometry mapping remains challenging due to non-uniqueness and fine geometric features. This work presents a two-stage deformable-convolutional framework for reconstructing metal--insulator--metal resonator geometries from 80-dimensional absorption spectra. The spectrum is projected to a 150\times4\times4 latent representation and decoded into a 64\times64 resonator mask. Training combines supervised reconstruction with least-squares adversarial refinement initialized from the best supervised checkpoint. A three-run ablation compares deformable convolution with plain convolution, involution, Dynamic Conv, and ODConv under the same architecture. The proposed model achieves 20.79\pm0.31 dB PSNR and 0.8501\pm0.0082 SSIM, improving over plain convolution by 2.16 dB and 0.0831, respectively. It further achieves Dice 0.9623\pm0.0027, IoU 0.9342\pm0.0038, and boundary F-score 0.9550\pm0.0027. Spectral consistency evaluated using a frozen forward surrogate yields RMSE 0.0805\pm0.0013 and R^2=0.7923\pm0.0065. Learned offsets show stronger adaptive sampling at coarse and intermediate decoder stages. Overall, deformable sampling with supervised initialization and adversarial refinement improves spectrum-conditioned geometry reconstruction.