# A Deep Learning-Based Mapping Model for Three-Dimensional Propeller RANS and LES Flow Fields
## 1 Introduction
In the field of computer vision, deep convolutional neural networks (CNNs) have demonstrated their outstanding performance in tasks such as image classification [10], object detection [11], and semantic segmentation [12]. In natural language processing, recurrent neural networks (RNNs) and Long Short-Term Memory (LSTMs) networks have promoted deep learning to be applied in language models and machine translation. Overall, deep learning, through continuously evolving neural network architectures, has provided powerful tools for various industries, driving rapid advancements in science and technology innovation. In turbulence flow analysis, machine learning has begun to be employed in recent years [13; 14]. The integration of machine learning with turbulence models has become a new direction in the field of fluid mechanics. Concurrently, the application of machine learning in RANS and LES models has brought about new possibilities for the research on fluid mechanics. For RANS models, machine learning methods have predominantly enhanced the efficiency and accuracy of numerical simulations and played a significant role in engineering design and research on fluid mechanics [15]. In LES simulations, the introduction of machine learning techniques has strengthened the prediction performance of models, aiding in the modeling of large-scale eddy structures [16]. These applications have been driving innovation in the field of fluid mechanics. By improving model accuracy and reducing computational costs, they provide more reliable numerical simulation tools for engineering design and scientific research. This study explores the application of machine learning, particularly deep learning techniques, to model turbulent flow fields. It focuses mainly on the mapping problem from the perspective of deep learning and does not go deeply into solving the Navier-Stokes (N-S) equations. The main purpose of this paper is to maintain the computational efficiency of RANS while generating prediction results close to the LES level from the RANS data with the proposed mapping model and regress module so as to achieve efficient numerical simulation under complex flow fields. Specifically, as mentioned above, LES is suitable for more accurate simulation of large-scale turbulent structures but requires large computational costs, while RANS is suitable for large-scale engineering calculations but lacks the resolution of the coherent scales of fluid structures in comparison to LES. In view of these characteristics of current turbulence models, we propose a method of mapping the data of the RANS flow field to the data of LES by using deep learning techniques for the purpose of significantly reducing the computational cost required by the direct generation of LES data. Specifically, the deep learning mapping model is trained on the given RANS and LES flow field samples. After that, the trained mapping model is integrated with a regression module, and thus, together, they establish connections between the numerical values of the RANS flow field and the LES flow field. By using the mapping model and the regression module, we can produce the prediction for the LES flow field from RANS flow field data. Compared to the direct LES, this method of obtaining LES data from the RANS data can enhance the computational efficiency with acceptable prediction accuracy. Therefore, the novelty of this paper is that the proposed fast and deep learning-based mapping method from RANS data to LES data reduces the computational resource requirements of traditional methods under complex geometric conditions and solves the problem of imbalance between accuracy and computational cost in current turbulence modeling by LES. The paper is organized as follows. Section 2 reviews some related work. The proposed methods are presented in Section 3, and the experimental results and analyses are provided in Section 4. Finally, the paper is concluded in the last section.