# Deep Learning-Based FSS Spectral Characterization and Cross-Band Migration
## 4 Conclusions  
In this paper, the FSS periodic units were coded as 16 \(\times\) 16 \"0/1\" rotationally symmetric matrices, each coded unit was guaranteed to have randomness, and 26,000 sets of transmittance and reflectance spectra in the range of 0.5-3 THz were collected as a dataset using the joint simulation of COMSOL and MATLAB. A 19-layer convolutional neural network was used to realize the FSS spectrum prediction, the average absolute error of the test set was as low as 0.06 and the single prediction time was as low as 0.09 s. In addition, the effects of various geometrical and material parameters of the FSS on the  
Figure 11: Comparison of transfer learning neural network results. (**a**–**d**) Training set. (**e**–**h**) Test set.  
spectral characteristics of the FSS were analyzed in detail and conclusions were drawn as follows: (1) when the metal thickness of the FSS is larger than its skinning depth, the spectral characteristics of FSSs with different metal types and thicknesses are similar; (2) the resonance frequency of the FSS was shifted by equivalent dielectric constant with different thicknesses of substrates; and (3) when the period length of the FSS was scaled at the same time and the highest frequency of incident, and the electromagnetic wave was the same multiple, the spectrum curves of FSS before and after scaling were similar for pure metal FSS with the same shape.  
On this basis, 6000 sets of millimeter-band FSS data were re-collected using COMSOL and MATLAB joint simulation, the already trained convolutional neural network in the THz band was used to transfer learning the data, which can achieve a comparable training effect with the former one after 1 min 14 s training time, and the average absolute error of the test set was 0.07. This study innovatively extended the cross-fusion of deep learning and FSSs from solving a specific problem to solving a certain class of problems.  
The dataset in this study was initially designed with a focus on universality, endowing the Frequency Selective Surface (FSS) codes with two fundamental characteristics: element-wise stochasticity and global rotational symmetry. These intrinsic properties impose significant challenges for neural networks in inverse design tasks, requiring simultaneous generation of randomly distributed unit elements while maintaining strict rotational symmetry at the macro level. Experimental results demonstrate that conventional convolutional neural networks (CNNs) fail to accomplish this dual-constrained generation task. Although transformer-based architectures show potential in producing qualified FSS codes that satisfy both geometric requirements, the spectral response curves of generated patterns still exhibit non-negligible deviations from the original designs, indicating the necessity for further accuracy improvements. Future work will focus on three critical directions: expanding the training dataset scale; optimizing algorithm architectures and modelling addresses that influence geometric and material parameters on spectral responses, which is fundamental to the design of FSS; and a method to improve the robustness of the numerical simulation of FSS by introducing error correction strategies based on physical models [31].  
Conceptualization, L.G. and Z.Y.; methodology, L.G.; formal analysis, P.Z. and X.L.; writing original draft preparation, X.L.; writing--review and editing, Z.Z and L.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Youth Innovation Team of Shaanxi Universities, grant number K20220184; the Key Scientific Research Plan of the Education Department of Shaanxi, grant number 23Y035; and the Natural Science Foundation of Shaanxi Province, grant number 2024 JC-YBMS-523.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author [PERSON] upon reasonable request.  
The authors sincerely appreciate all financial and technical support.  
The authors declare no conflicts of interest.