## 3 Machine Learning Techniques
### Validation of Machine Learning Model
In Table 6, the resulting antenna models can be divided into two types in geometry: one type is the monopole antenna with a top load such as the inverted-L antenna (the antennas with the ranks 6 and 9 in Table 6) and the other type is the monopole antenna with a middle load (the antennas with the ranks 1-5, 7-8, and 10 in Table 6). Thus, to further study two types of antennas, we examined the radiation pattern and the impedance matching characteristics of both types of antennas having the ranks 1 and 6 in Table 6 using NEC and commercial EM simulators [45]. From the simulated results, we confirmed that both antennas have a radiation pattern similar to that of an ideal monopole antenna. In addition, we represent the simulated reflection coefficients of both antennas as a function of frequency in Figure 5, where the configuration of both antennas is illustrated in the insets. Although there is a small discrepancy in reflection coefficient owing to the applied analysis methods (NEC using the moment of method and Femtet using the finite element method), the result of Figure 5 implies that both types of antennas operate well with small reflection coefficients in the interesting frequency range from 950 to 1050 MHz. This result also validates our ML model that can predict the impedance matching characteristic of the monopole antenna formed by a bent wire. Based on the geometry depicted in the insets of Figure 5, we represent the monopole antennas with top load and middle load in Figure 6 as possible equivalent circuits [46; 47; 48; 49; 50]. We expressed the vertical and horizontal wire sections as series and parallel RLC circuits, respectively. In addition, we assigned the parallel capacitance (\(C_{h2}\)) caused by the open end of the antenna arm to the possible equivalent circuit. The series capacitance (\(C_{p}\)) is negligible due to the current flowing along the vertical wire section. Thus, the parallel capacitances (\(C_{h1}\) and \(C_{h2}\)) derived from the loads and the open end dominantly influence the impedance matching because it cancels out the series inductance (\(L_{c1}\)) yielded by the vertical wire section. In the case of a monopole antenna with a middle load, we found that the basic operating principle is similar to that of a monopole antenna with a top load. Although the contribution of the second vertical wire section (third wire section) to the antenna impedance is small, we think it may finely control the induced current affecting antenna impedance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Design Parameters**} & \multicolumn{6}{c}{_AF (\%)/Cost_} \\ \cline{2-9}
**Rank** & \multicolumn{3}{c}{**Unit: mm**} & \multicolumn{3}{c}{**Unit: degree**} & \multicolumn{3}{c}{**ML Model**} & \multicolumn{1}{c}{**NEC Simulator**} \\ \cline{2-9}  & \(I_{1}\) & \(I_{2}\) & \(I_{3}\) & \(\theta_{1}\) & \(\theta_{2}\) & \(\theta_{3}\) & & \\ \hline
1 & 49.3 & 9.0 & 9.0 & 90.0 & 14.7 & 90.0 & 78.76/42.70 & 78.58/43.05 \\
2 & 49.3 & 9.0 & 9.0 & 90.0 & 10.0 & 85.3 & 78.71/42.79 & 78.49/43.24 \\
3 & 49.3 & 9.0 & 9.0 & 90.0 & 14.7 & 85.3 & 78.70/42.80 & 78.46/43.30 \\
4 & 49.3 & 9.0 & 9.0 & 90.0 & 19.4 & 90.0 & 78.66/42.89 & 78.49/43.24 \\
5 & 49.3 & 9.0 & 9.0 & 90.0 & 10.0 & 80.6 & 78.66/42.89 & 78.39/43.44 \\
6 & 32.7 & 23.2 & 11.4 & 90.0 & 90.0 & 10.0 & 78.63/42.95 & 77.90/44.42 \\
7 & 49.3 & 9.0 & 9.0 & 90.0 & 19.4 & 85.3 & 78.63/42.96 & 78.33/43.56 \\
8 & 49.3 & 9.0 & 9.0 & 90.0 & 14.7 & 80.6 & 78.62/42.98 & 78.32/43.58 \\
9 & 35.1 & 20.8 & 11.4 & 90.0 & 90.0 & 10.0 & 78.61/42.99 & 77.97/44.28 \\
10 & 49.3 & 9.0 & 9.0 & 90.0 & 24.1 & 90.0 & 78.61/43.00 & 78.30/43.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Design parameters of the ranked antenna models in terms of \(AF\) when searching antenna models on the entire grid.