# A Deep Learning-Based Mapping Model for Three-Dimensional Propeller RANS and LES Flow Fields
## 5 Conclusions  
In this work, we proposed a model for mapping between RANS and LES data based on deep learning methods. The model first voxelized the two types of flow field data to generate their corresponding three-dimensional graphical data. Then, it establishes a mapping relationship by using deep convolutional neural networks and combines regression modules to regress the flow field data. Experimental results showed that the model accurately predicted LES results based on RANS simulation data, with an error rate of only 17.68%. By comparing the model's predicted results with actual RANS and LES simulation results, we observed significant improvements in accuracy and computation efficiency. Additionally, the model demonstrates good generalization under different Reynolds numbers. The method proposed in this work provides a new path for turbulence research. It not only retains the low computational cost advantage of the RANS method but also improves the accuracy of flow field simulation by deep learning technology. It provides new ideas for turbulence research based on numerical simulation and is of great significance for revealing complex turbulent flow phenomena.  
Despite the advantages in accuracy and efficiency, the proposed model also has some limitations. Firstly, its performance is constrained by limited training data and coverage of data ranges, so it is unable to cover all propeller operating conditions and design scenarios. Secondly, deep learning models require significant computational resources, which may limit their applicability in resource-constrained environments. Furthermore, the black-box nature of the model may raise concerns related to interpretability and credibility. Challenges related to universality, uncertainty modeling, and other aspects need further work and improvement. Therefore, it is necessary to consider these limitations comprehensively in practical engineering applications.  
In conclusion, this work successfully implements the mapping of three-dimensional RANS and LES flow fields based on deep learning methods, with positive results achieved. It provides a valuable example of applying deep learning in the field of fluid dynamics and introduces new ideas and methods for handling complex turbulence modeling problems.  
In the future, we will focus on using the methods suggested in the discussion to improve the model's prediction accuracy in propeller blade edges and other complex flow field regions.  
Conceptualization, J.J.; Methodology, J.J.; Validation, X.L.; Formal analysis, Y.Y.; Investigation, Y.Y. and J.S.; Resources, L.L.; Data curation, Y.Y.; Writing--original draft, Y.Y.; Writing--review and editing, J.J. and J.S.; Visualization, M.S.; Supervision, J.S.; Project administration, J.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the development and application project of ship CAE software and the National Natural Science Foundation of China under Grants 62272202 and 61672263.  
Not applicable.  
No new data were generated in this study.  
The authors declare no conflicts of interest.