# A Mapping Model of Propeller RANS and LES Flow Fields Based on Deep Learning Methods
## 1 Introduction
The first one is based on the framework of theoretical models, where an ideal system description is made according to the governing equations of the physical problem. This type of model typically requires researchers to have a deep understanding of the physical processes and be able to translate them into mathematical models. Most of the current turbulence models, such as the k-\(\omega\) model [7] and the Spalart-Allmaras (SA) model [8], are developed by using this approach. The second type is based on data-driven approaches, which involve direct construction of black-box or grey-box models based on sample data obtained from system simulations or experiments. How to effectively utilize large datasets, extract key information from them, and guide the development of fluid mechanics have become focuses of researchers' attention. Machine learning techniques, such as radial basis function neural networks (BRFNN), random forests (RF), support vector machines (SVM), and neural networks (NNS), have been widely applied in many areas such as speech and image recognition [9; 10], signal processing [11], and model reduction [12]. The combination of machine learning and turbulence modeling has become an emerging research direction in the field of fluid mechanics. Existing research findings have strongly validated its feasibility and indicate the positive prospects of machine learning in future applications of turbulence modeling [13]. However, there are still many challenges and unsolved problems in this field. For instance, how to improve the generalization ability, robustness, and stability of the models is the main concern of researchers. Existing studies showed that the model performance tends to degrade to varying degrees when there are significant differences between the predicted data and the training data or when there are changes in the geometric shape. This is to some extent an inherent limitation of data-driven methods. Additionally, some aspects in the model construction, such as data processing and feature engineering, selection of model objects, and constraint conditions, can also influence the final performance of the models. Therefore, in order to address the challenges of complex system modeling and to partially overcome the issues encountered in applying machine learning to turbulence, this paper proposes a sample mapping model for simulating the flow field of a propeller by using a deep-learning-based approach to combining Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES). The model is constructed by training on existing RANS and LES flow field samples, with the mapping between numerical values of simulation samples for propeller flow fields. By learning the mapping relations between RANS and LES, we can obtain flow field predictions close to those predicted via LES but with higher computational efficiency. The contributions of this paper can be summarized as follows. First, we propose a novel, neural-network-based mapping method of transforming RANS data to LES data, addressing the issues associated with both simulation methods. Second, we extensively evaluate the performance of several neural network models for feature extraction on a dataset comprising over a thousand sets of RANS and LES simulated data of swirling flow fields. Finally, we demonstrate the generalization capability of our model by applying it to two-dimensional swirling flow field simulation data generated at different Reynolds numbers. 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 3. Finally, the paper is concluded in the last section.