# A Deep Learning-Based Mapping Model for Three-Dimensional Propeller RANS and LES Flow Fields
## 4 Experiments
### Experiment of Feature Extraction Model for Flow Fields
#### 4.3.3 Experiments of Mapping Model Input  
In this set of experiments, we primarily investigated different input types in the mapping neural network and summarized the findings in Table 2. The results indicate that although the dual-stream network incurred additional time overhead to compute optical flow, there is no improvement in mapping results. This suggests that in three-dimensional space, additional temporal features may not be better for the mapping of turbulent data. In addition, while the input of a single velocity component showed comparable overall time overhead to the input of three velocity components, it exhibited slightly higher error rates. Therefore, we conclude that the input of three velocity components is more suitable for mapping three-dimensional turbulent flow models. Moreover, it is evident that almost all results show a significantly lower error rate for _V_axial_ compared to _V_tangential_ and _V_radial_. After analyzing the RANS and LES data, we found that the mean and variance of velocity for _V_axial_ were much larger than those for _V_tangential_ and _V_radial_, which indicates smaller velocity variations for _V_tangential_ and _V_radial_. Consequently, both voxelization and mapping networks struggled to accurately fit the data characteristics, particularly for _V_tangential_ and _V_radial_. Additionally, due to the normalization operation required during the neural network's data preprocessing, which involves subtracting the mean and dividing by the variance, the prediction deviation for the three velocity components was disproportionately amplified due to normalization, leading to the current situation after the calculation of customized error rate formulas. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Input Size** & **Voxel Size** & **Time of Voxel** & **V\_axial** & **V\_tangential** & **V\_radial** & **Average** \\
**(m)** & **(m)** & **Generation(s)** & **Error Rate** & **Error Rate** & **Error Rate** & **Error Rate** \\ \hline \(1\times 1\times 0.5\) & 0.01 \(\times\) 0.01 \(\times\) 0.01 & 336 & 2.87\% & 26.94\% & 22.54\% & 693 \\ \(1\times 1\times 0.5\) & 0.0125 \(\times\) 0.0125 \(\times\) 0.0125 & 292 & 3.04\% & 27.75\% & 34.59\% & 589 \\ \(0.9\times 0.9\times 0.5\) & 0.01 \(\times\) 0.01 \(\times\) 0.01 & 315 & 2.71\% & 27.12\% & 22.58\% & 626 \\ \(0.8\times 0.8\times 0.4\) & 0.01 \(\times\) 0.01 \(\times\) 0.01 & 269 & 2.76\% & 27.55\% & 22.60\% & 542 \\ \(0.8\times 0.8\times 0.4\) & 0.0125 \(\times\) 0.0125 \(\times\) 0.0125 & 230 & 2.73\% & 27.59\% & 22.73\% & 467 \\ \(0.8\times 0.8\times 0.4\) & 0.02 \(\times\) 0.02 \(\times\) 0.01 & 153 & 3.64\% & 35.57\% & 30.86\% & 315 \\ \(0.7\times 0.7\times 0.4\) & 0.01 \(\times\) 0.01 \(\times\) 0.01 & 217 & 3.17\% & 29.83\% & 25.43\% & 420 \\ \(0.6\times 0.6\times 0.4\) & 0.01 \(\times\) 0.01 \(\times\) 0.01 & 173 & 3.18\% & 30.62\% & 28.89\% & 354 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of experimental results with different sizes of input flow field and voxel sizes. Upon comparing the experimental results, we found that the introduction of the dual-stream network did not improve the mapping of three-dimensional graphical data. Instead, it led to an increase in error rates, contrary to the results observed in the two-dimensional experiments. To verify whether the issue stemmed from dataset differences, we extracted the central region of the propeller from the three-dimensional data and fixed the position at \(x=0.012\). Approximately 20,000 points were selected at this interface position for the two-dimensional experiment, and the final experimental results are shown in Table 3.  
The comparison of the experimental results demonstrates that the dataset conforms to the mapping rules of two-dimensional data proposed in the previous work within the central region of the propeller. However, upon comparing the optical flow information of two-dimensional and three-dimensional inputs, it was observed that the optical flow of three-dimensional data is more complex.