# Metamaterial Design with Nested-CNN and Prediction Improvement with Imputation
## 4 Results and Discussion  
The success of Model-2 was evaluated by using MAE, the R2 score, and mean correlation coefficients for validation data and test data. The R2 score of Model-2 was 0.96. For Model-2, the MAE of training data, test data and validation data are given in Table 4.  
The similarity between Model-2's result and the result of the simulation was measured by using correlation coefficients. The mean of the correlation coefficients was used for \begin{table}
\begin{tabular}{c c c c} \hline  & **MAE** & **Validation MAE** & **Test MAE** \\ \hline
**Model-2** & 0.22 & 0.26 & 0.27 \\ \hline \end{tabular}
\end{table} 
Table 4: Mean absolute error of Model-2. Figure 4: An example of the region of interest and the non-interested region. validation data and test data by comparing the results of Model-2 and the simulation program. The mean correlation coefficient for test and validation data is given in Table 5.  
Five images of MM were used to compare Model-2's result and the simulation's result. These images have never been seen by Model-2 in the training process. In Figure 5, the first column corresponds to the randomly generated image of MM, the second column corresponds to the reflection coefficients of Model-2, and the reflection coefficient of simulation. The orange line represents Model-2's result, and the blue line represents the simulation results. Early stopping was monitoring MAE of validation for Model-2 and was stopped training at the 63 rd epoch to prevent overfitting to training data. Training error and validation error for Model-2 are shown in Figure 6.  
Figure 5: Five random examples of Model-2. The orange line represents Model-2’s result, and the blue line represents the simulation results. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Mean Correlation Coefficient of the Reflection Coefficient**} \\ \hline
**Test data** & 0.93 \\
**Validation data** & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean correlation coefficient results of Model-2 and simulation based on test data. The nested-CNN's performance was evaluated with MAE and R2 scores. The MAE of trained data, test data and validation data are given in Table 6. The R2 score of the nested-CNN was 0.9. The following situation should not be overlooked--the nested-CNN accepts the error margin of Model-2 used in the creation loss value in the training process as 0. In this case, nested-CNN's margin of error should be considered as the MAE of the nested-CNN and the sum of the MAE of Model-2. Early stopping was monitoring the MAE of desired reflection coefficient and the reflection coefficient of the produced image of MM. The nested-CNN was stopped at the 45 th epoch to prevent overfitting by early stopping. Training loss and validation loss graphics are given in Figure 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MAE** & **Validation MAE** & **Test MAE** \\ \hline
**Nested-CNN** & 0.32 & 0.40 & 0.42 \\
**Nested-CNN + MAE of Model-2** & 0.54 & 0.66 & 0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean absolute error of nested-CNN after training process, the MAE of the nested-CNN by considering the MAE of Model-2. Figure 6: Training Loss and Validation Loss of Model-2. The nested-CNN's performance was evaluated with six desired reflection coefficients. Desired reflection coefficient maximum value was chosen as \(-5\) dB, the minimum value was chosen lower than \(-40\) dB, the minimum bandwidth was chosen as 0.75 GHz. In Figure 8, the desired reflection coefficients, the image of MM--which is gradient-based generated by nested-CNN--and the simulation results of the image of MM are given. Figure 7: Training loss and validation loss of the nested-CNN. Figure 8: \(Cont.\)  
The performance of the KNN-imputer for prediction depends on the count of the neighbors, the count of the dataset, and the samples count of the non-interested region. Moreover, the count of the neighbors depends on the samples count and the count of the dataset.