## 3 Numerical Results  
Here, we report the numerical results obtained following the illustrated methodology (Figure 3). First of all, the validation LOO-CV errors (Equation (7)) have been computed for the obtained surrogate models based on the results of \(N=60\) simulations, i.e., 60 different combinations of beamforming scan angles. The error values are reported in Table 1. They ranged from a minimum of 0.27%, computed for the average \(SAR\) in the whole head, to a maximum of 5.70% for the \(SAR_{10g}\) in the cerebellum, thus proving sufficiently low error values to validate the model. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{1}{c}{**Whole Body**} & **Whole Head** & **Whole Brain** & **Skin** & **Brain Grey Matter** & **Cerebellum** \\ \hline
**LOO Error** & 0.31\% & 0.27\% & 0.94\% & 2.85\% & 2.06\% & 5.70\% \\ \hline \end{tabular}
\end{table} 
Table 1: LOO-Error values of the surrogate models for tissue average \(SAR\) in the whole body, whole head, and whole brain and for \(SAR_{10g}\) in skin, brain grey matter, and cerebellum. Once the surrogate models were validated, they were used to estimate the exposure levels in terms of both average \(SAR\) and maximum \(SAR_{10g}\) for 1000 different combinations of azimuth and elevation angles of the main radiation beam. Figures 4 and 5 and Table 2 refer to the average \(SAR\) results on the whole body on the whole head and on the whole brain, while Figures 6 and 7 and Table 3 refer to maximum \(SAR_{10g}\) results on the skin, on the brain grey matter and on the cerebellum. The exposure levels are estimated for a total input power of the UPA antenna equal to 100 mW. Figure 4: Boxplots of the averaged \(SAR\) values obtained for 1000 combinations of the two input scan angles mediated (**a**) on the whole body, (**b**) on the whole head, and (**c**) on the whole brain. The lower and upper bound of the boxes represent the first and the third quartiles, the line is the median value, and the whiskers are the minimum and maximum values. Figure 5: Averaged \(SAR\) levels for 1000 combinations of azimuth and elevation angles for (**a**) the whole body, (**b**) the whole head, and (**c**) the whole brain tissue. The first row shows the maps as function of the azimuth and elevation angles; the second row shows the graphs, extracted from the maps, fixed the elevation angle to 0\({}^{\circ}\); the third row shows the graphs, extracted from the maps, fixed the azimuth angle to 0\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Whole Body** & **Whole Head** & **Whole Brain** \\ \hline
**QDC** & 71.7\% & 73.5\% & 74.8\% \\
**\% > 0.7 maximum** & 7.2\% & 4.7\% & 3.3\% \\
**Range H-plane** & From \(-7^{\circ}\) to \(7^{\circ}\) & From \(-8^{\circ}\) to \(6^{\circ}\) & From \(-6^{\circ}\) to \(7^{\circ}\) \\
**Range E-plane** & From \(-22^{\circ}\) to \(7^{\circ}\) & From \(-10^{\circ}\) to \(7^{\circ}\) & From \(1^{\circ}\) to \(7^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The QDC values, the percentage of _SAR_ values higher than the 70% of the maximum values, and the corresponding ranges of elevation and azimuth angles for whole body, for whole head, and for whole brain. Figure 6: Boxplots of the maximum _SAR_ values mediated on 10 g obtained for 1000 combination of the two input scan angles (**a**) on the skin, (**b**) on the brain grey matter, and (**c**) on the cerebellum. The lower and upper bounds of the boxes represent the first and the third quartiles, the line is the median value, and the whiskers are the minimum and maximum values. Figure 7: Maximum SAR levels mediated on 10 g for 1000 combinations of azimuth and elevation angles for (**a**) the skin, (**b**) the grey brain matter, and (**c**) the cerebellum. The first row shows the maps as a function of the azimuth and elevation angles; the second row shows the graphs, extracted from the maps, fixed the elevation angle to \(0^{\circ}\); the third row shows the graphs, extracted from the maps, fixed the azimuth angle to \(0^{\circ}\).