## 3 Results
### Evaluation of Dose Distributions
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \multicolumn{2}{c}{**Plan**} & \multicolumn{2}{c}{**P1**} & \multicolumn{2}{c}{**P2**} & \multicolumn{2}{c}{**HN1**} & \multicolumn{2}{c}{**HN2**} \\ \hline
**Phase Space** & **GPR** & \(\mathbf{\Delta D_{5}}\) & \(\mathbf{\Delta D_{95}}\) & **GPR** & \(\mathbf{\Delta D_{5}}\) & **\(\mathbf{\Delta D_{95}}\)** & **GPR** & \(\mathbf{\Delta D_{5}}\) & **\(\mathbf{\Delta D_{95}}\)** & **GPR** & \(\mathbf{\Delta D_{5}}\) & \(\mathbf{\Delta D_{95}}\) \\ \hline \multirow{9}{*}{CGAN} & \(P_{0}\) & 96.99 & 0.01 & 0.40 & 97.68 & 0.66 & 3.00 & 98.87 & 1.03 & 2.74 & 98.85 & 0.71 & 1.16 \\  & \(P_{1}\) & 96.66 & 0.20 & 0.09 & 98.06 & 0.89 & 2.34 & 99.24 & 0.21 & 1.85 & 98.65 & 0.48 & 0.56 \\  & \(P_{2}\) & 97.74 & 0.15 & 0.19 & 98.40 & 0.78 & 2.15 & 99.63 & 1.19 & 3.49 & 99.11 & 0.42 & 0.53 \\  & \(P_{3}\) & 96.30 & 0.26 & 0.50 & 97.05 & 0.76 & 3.18 & 98.08 & 1.19 & 2.66 & 98.71 & 0.32 & 1.02 \\  & \(P_{4}\) & 93.99 & 0.06 & 0.78 & 97.08 & 0.60 & 2.76 & 95.12 & 1.92 & 2.10 & 97.10 & 1.26 & 1.84 \\  & \(P_{5}\) & 94.87 & 0.55 & 0.48 & 98.67 & 0.94 & 2.52 & 99.70 & 0.36 & 1.51 & 99.02 & 0.71 & 0.82 \\  & \(P_{6}\) & 97.23 & 0.61 & 0.78 & 98.96 & 0.74 & 2.00 & 99.75 & 0.27 & 1.36 & 99.14 & 0.69 & 0.87 \\  & \(P_{7}\) & 97.95 & 0.02 & 0.50 & 98.02 & 1.15 & 2.56 & 98.53 & 1.30 & 2.09 & 98.89 & 0.49 & 0.87 \\  & \(P_{8}\) & 98.70 & 0.01 & 0.31 & 99.05 & 0.70 & 2.07 & 99.67 & 0.98 & 1.04 & 99.50 & 0.55 & 0.82 \\  & \(P_{9}\) & 98.05 & 0.01 & 0.35 & 98.57 & 0.68 & 2.42 & 99.80 & 0.47 & 1.68 & 99.27 & 0.46 & 0.56 \\ \hline \multirow{9}{*}{RoCGAN} & mean & 96.85 & 0.19 & 0.44 & 98.15 & 0.79 & 2.50 & 98.84 & 0.89 & 2.05 & 98.82 & 0.61 & 0.91 \\  & std & 1.40 & 0.21 & 0.21 & 0.68 & 0.15 & 0.37 & 1.36 & 0.52 & 0.70 & 0.62 & 0.25 & 0.37 \\ \hline \multirow{9}{*}{CGAN} & \(P_{0}\) & 97.98 & 0.11 & 0.11 & 98.33 & 0.28 & 1.09 & 99.78 & 0.25 & 0.54 & 99.28 & 0.14 & 0.27 \\  & \(P_{1}\) & 97.38 & 0.21 & 0.29 & 98.32 & 0.20 & 2.08 & 99.80 & 0.18 & 2.01 & 99.29 & 0.14 & 0.10 \\  & \(P_{2}\) & 97.19 & 0.31 & 0.60 & 98.28 & 0.28 & 1.79 & 99.81 & 0.17 & 1.22 & 98.96 & 0.37 & 0.53 \\  & \(P_{3}\) & 97.87 & 0.16 & 0.19 & 98.26 & 0.38 & 2.16 & 99.80 & 0.12 & 1.79 & 99.37 & 0.03 & 0.18 \\  & \(P_{4}\) & 97.89 & 0.08 & 0.08 & 98.21 & 0.23 & 1.58 & 99.78 & 0.31 & 1.50 & 99.25 & 0.16 & 0.01 \\  & \(P_{5}\) & 93.06 & 0.76 & 0.93 & 98.54 & 0.38 & 0.54 & 99.83 & 0.27 & 1.29 & 99.07 & 0.72 & 0.86 \\  & \(P_{6}\) & 97.55 & 0.57 & 0.77 & 99.06 & 0.44 & 1.11 & 99.79 & 0.27 & 1.66 & 99.34 & 0.53 & 0.64 \\  & \(P_{7}\) & 99.06 & 0.04 & 0.08 & 98.61 & 0.44 & 2.07 & 99.85 & 0.27 & 2.08 & 99.51 & 0.06 & 0.13 \\  & \(P_{8}\) & 99.24 & 0.10 & 0.07 & 99.27 & 0.23 & 1.96 & 99.8 Figure 4: Dose profiles calculated from the PRIMO-generated phase space and GAN-generated phase space, with bands representing two standard deviations of dose uncertainty, as reported by PRIMO. **(a–d)** Depth profiles at beam axis. **(e–h)** Lateral profiles along the Y axis at depth 6.9 cm. In panels **(a,b,e,f)** are shown profiles for which the RMS value was the lowest among all test phase spaces. The remaining four profiles are those for which the corresponding RMS value was the highest. All profiles have been normalized to 1.0 relative dose at 6.9 cm beam depth in water.