# A Deep Learning-Based Mapping Model for Three-Dimensional Propeller RANS and LES Flow Fields
## 4 Experiments
### Discussion
In fact, we made efforts to minimize the error and improve the model's ability to predict complex flow fields through deep learning model training and diversified sample input. Although the error exceeded the acceptable range of 3-7% in some cases, the method still showed through a large number of experiments that the overall error rate was within a certain range (about 17.68%), and most of the errors were concentrated on the edges of complex propeller blades. To enhance credibility, the model uses large-scale RANS and LES sample mapping to calibrate the flow field characteristics so that the output is closer to the details of the LES. In addition, the authors adopted an adaptive optimization algorithm and an error-weighted training mechanism to increase the optimization efforts in larger error areas and ensure the accuracy of the overall trend and main flow field characteristics. Therefore, under the premise of understanding the source and area of the error, the prediction results of the model are still practical in engineering. Secondly, it can be found that there are some cases where the error rates are relatively higher, especially in some complex flow areas, such as the propeller blade edges. This is due to the presence of vortices and small-scale eddies since the local velocity field can be affected and flow field complexity is increased, which makes the model predictions have higher errors. In order to improve the model, the following measures can be taken: First, we can enhance the edge feature learning by introducing edge detection modules or edge-weight penalties in the training process to make the model focus more on learning features in complex blade edge regions. Second, data augmentation can be undertaken by adding more samples with complex vortex and flow separation characteristics to the training data to improve the model's adaptability to different flow field features. Third, we can use multiscale convolution layers to increase the model's sensitivity to vortices and flow field changes at various scales so that the model's ability to learn both detailed and global features can be enhanced. Besides, for areas with large errors, we could conduct a comparative analysis of velocity distribution and flow features between RANS and LES to identify potential physical factors causing errors, such as nonlinear flow effects and fluid-structure interactions. Based on the analysis, we can adjust model parameters, optimize the loss function (e.g., adding position-related weights), or refine training methods for targeted model improvement. Thirdly, it should be noted that For RANS data lacking coherent structures, the model proposed in this paper uses the feature extraction ability of deep learning to recognize and map coherent structures and effectively overlay them on LES data. The model employs a deep learning model based on a mapping model to perform in-depth feature extraction and mapping on RANS and LES data. Although RANS data itself has no obvious, coherent structure, the deep learning model can learn potential patterns and features from it, thereby generating complex structures similar to LES flow fields. After the mapping process, the regression algorithm predicts the coherent structure of a specific location in the flow field based on the LES image mapped from the RANS image by the model obtained by the training phase. Therefore, even if the RANS data itself is insufficient, the model can still present the details and turbulence characteristics in the output of LES data. In addition, the powerful mapping ability of deep learning ensures that the mapping model can learn the nonlinear relationship between the two flow fields through training on a large number of RANS and LES samples. Even turbulent features that are not directly reflected in RANS data can be reproduced and generated in the model's predictions.