Fast Scattering Prediction for Deformed Metasurfaces Using a Fourier-Encoded Neural Surrogate

6G networks are expected to use the upper mid-band (FR3, 7–24 GHz), where higher path loss and blockage by buildings become significant limitations, leaving drones in urban airspace with an intermittent link to ground infrastructure. Metasurfaces offer a low-cost way to restore coverage by redirecting the incident wave, but the panels deform under thermal and mechanical loading. Structural simulation predicts 0.55 mm of deformation under a worst-case thermal assumption, at which the scattering cross-section changes by up to 1.3 dB across the observation angles; at 5 mm the median change reaches 3.1 dB with a beam shift of up to 1.4°. Predicting this requires a full-wave solve for the surface current, taking 10 s to 9735 s across the parameter grid, followed by 6.2 s of radiation integration per scattering pattern.

This work presents a neural surrogate mapping the deformation state, incidence and observation angles, and frequency onto the bistatic scattering cross-section, with the deformation parameterized by analytical modal shape functions verified against structural finite element simulations. The oscillatory inputs are expanded onto a Fourier basis, and the contribution lies in how the bandwidth of that basis is set: rather than being tuned as a hyper-parameter, the angular order is taken from the Fourier spectrum of the response (K = 60) and the frequency order from the Nyquist limit of the 26 frequency samples (K_f = 13). A grid search over K required four training runs, about 78 minutes, to locate the value that a single fast Fourier transform (FFT) identifies in 0.02 ms. Trained on 3494 curves, the surrogate reproduces the full lobe structure to within 0.42 dB and evaluates a complete 401-point pattern in 7.25 ms (median of 1000 runs), about 850 times faster than the 6.2 s required for the radiation integral alone.