# Meander Structure Analysis Techniques Using Artificial Neural Networks
## 3 Results
### Results Obtained with Convolutional Neural Network  
A visual representation of the predictions of \(t_{\text{d}}\), \(S_{21}\), and \(S_{11}\) using a CNN is presented in Figure 8. The dashed lines represent the predicted characteristics, while the straight lines represent the target characteristics. The prediction results were obtained by training three individual CNN models. For each figure, four prediction results from the test set are visualized. The meander structures and their indexes in the figures were the same as in the previous subsections and are given in Table 1. CNN training depends mainly on the batch size and maximum epoch number, and for this research, the training of a CNN for a single characteristic lasted approximately 90 s, and the prediction time was approximately 0.13 s.  
Figure 7(a) provides an overview of the frequency-dependent behavior in four configurations of meander structures, detailing the characteristic \(t_{\text{d}}\) for each setting. Visually, it can be observed that the predicted characteristics differed to the order of hundreds of nanoseconds when working within the 1 ns range. The MAE in the prediction of the characteristic \(t_{\text{d}}\) in the entire investigated frequency band when using the test set of the 74 unique testing structures was \(27.5\pm 3.5\) ps (Table 2) and \(27.7\pm 9\) ps for the displayed characteristics in Figure 7(a).  
Figure 7(b) provides an overview of the frequency-dependent behavior, detailing the characteristic \(S_{21}\) for each setting of the meander structure in the 0-10 GHz frequency range. Visually, it can be observed that there were minimal differences between the actual and predicted signals in the bandwidth, ranging from 0 to approximately 3 GHz. The MAE in the prediction of the characteristic \(S_{21}\) for all investigated frequencies when using the test set was \(0.44\pm 0.46\) dB (Table 2), and it was \(0.4\pm 0.31\) dB for the displayed characteristics in Figure 7(b).  
Figure 7: The (a) \(t_{\text{d}}\), (b) \(S_{21}\), and (c) \(S_{11}\) characteristics of MS2 when the (6-9-11-1) TDNN structure was used for \(t_{\text{d}}\) prediction and (6-9-16-1) TDNN structure was used for \(S_{21}\) and \(S_{11}\) prediction, with a delay buffer \(N_{\text{d}}\) equal to 1, 2, 4, or 8.  
Figure 8c provides an overview of the frequency-dependent behavior, detailing the characteristic \(S_{11}\) for each setting of the meander structure. In the figure, a dynamically changing region is highlighted. When comparing the predicted and actual values of the characteristic \(S_{11}\), particularly when \(S_{11}\) was close to 0 dB, the differences between the two sets of values were minimal. The MAE in the prediction of the characteristic \(S_{11}\) throughout the investigated frequency band when using the test set was 1.36 \(\pm\) 0.72 dB (Table 2), and it was 1.2 \(\pm\) 1.18 dB for the displayed characteristics in Figure 8c,d.  
The summarized prediction accuracy results in terms of MAE with an SD for \(t_{\text{d}}\), \(S_{21}\), and \(S_{11}\) in the overall 74 MS training set are presented in Table 2.  
The MAEs with the SDs for \(t_{\text{d}}\), \(S_{21}\), and \(S_{11}\) were also compared with those for the baseline LSBoost method. The best \(t_{\text{d}}\) and \(S_{21}\) prediction results were achieved with the TDNN network when \(N_{\text{d}}\) = 8. The best \(S_{11}\) prediction results were achieved with the CNN network.