# A Deep Learning-Based Mapping Model for Three-Dimensional Propeller RANS and LES Flow Fields
## 4 Experiments
### Experiment of Regression of Flow Fields  
Through the experimental results presented above, we utilized a region around the propeller of size 0.8 \(\times\) 0.8 \(\times\) 0.4 (unit: meters) and performed voxelization by using grids of size 0.0125 \(\times\) 0.0125 \(\times\) 0.0125 (unit: meters), which resulted in a 64 \(\times\) 64 \(\times\) 32-sized three-dimensional array. We employed the fusion of three velocity components as the input to the feature mapping network and performed regression to compute all velocity information for the final mapping results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model Input** & **V\_axial** & **V\_tangential** & **V\_radial** & **Average Prediction Time (s)** \\  & **Error Rate** & **Error Rate** & **Error Rate** & **Average Prediction Time (s)** \\ \hline Single Velocity & & & & \\ Component & 2.75\% & 27.55\% & 22.89\% & 473 \\ Three Velocity & & & & \\ Component & 2.73\% & 27.59\% & 22.73\% & 467 \\ Time-stream + Single & & & & \\ Velocity Component & 5.56\% & 41.27\% & 69.83\% & 542 \\ Time-stream + Three & & & & \\ Velocity Components & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of mapping network error rates for different inputs. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Input** & **V\_axial Error Rate** & **V\_tangential Error Rate** & **V\_radial Error Rate** \\ \hline Time-stream + Three & & & \\ Velocity Components & 5.64\% & 7.78\% & 9.26\% \\ Three Velocity & & & \\ Components & 5.85\% & 8.42\% & 9.78\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental comparison of the two-dimensional interface at propeller center \(x=0.012\). Table 4 summarizes the overall mapping results on the dataset, comprising approximately 200 samples. In the experiments, we first generated two types of three-dimensional image data using RANS and LES, then trained the mapping module, and finally integrated them into a complete model for prediction. From the table, it can be observed that the average mapping error rate for the three velocity components is approximately 17.68%, indicating excellent model performance. Additionally, we interpolated the mapping results with the standard values to create interpolated plots, as shown in Figure 9. From the figures, it is evident that the primary errors in the predicted data are concentrated around the position of the propeller blade. We have extracted some data from the propeller center area and presented it in Table 5, which includes the \((x,y,z)\) coordinates of each point, along with the predicted and actual results for the three velocity components at those points. We also provide a detailed comparative analysis of the two-dimensional mapping network and the three-dimensional mapping network, with specific experimental results detailed in Table 6. The results indicate that the two-dimensional mapping model performs significantly better in terms of overall error rate, approximately 8%, compared to the 18% exhibited by the three-dimensional mapping network, showing a notable advantage. However, it is worth noting that this advantage comes with a longer time requirement for the two-dimensional mapping model. In the three-dimensional mapping model, due to the significant increase in the number of points, it is not feasible to use a regression network for each point individually, as in the two-dimensional mapping model. Instead, an integrated mapping network combined with the regression module is required to improve the time efficiency. However, this optimization strategy also leads to an increase in the overall error rate. Furthermore, since the three-dimensional mapping network handles more complex data, its model is usually more complicated. This complexity may make it more challenging for the model to converge during training and optimization, thereby increasing the error rate. Through extensive optimization efforts, our work successfully reduced the overall error rate to within 20%, essentially ensuring the accuracy of the mapping data.