# Fast Prediction of Flow Field around Airfoils Based on Deep Convolutional Neural Network
## 1 Introduction
As a result, large amounts of data are required to be fed to the model, making it difficult to deal with high-dimensional nonlinear problems. As an important branch of ML, deep learning methods are designed in the first place for high-dimensional nonlinear problems, typically coupled with massive data. Deep learning achieves great success in the area of computer vision, then rapidly attracts research attention in the field of structural and fluid mechanics [22; 23]. Specifically for aerodynamic design and optimization, deep learning has been applied to flow prediction [24; 25; 26; 27; 28; 29], flow field reconstruction [30; 31], modes classification [32], fault detection [33], and design optimization [34]. [PERSON] and [PERSON], for example, utilized deep learning to identify regions of high uncertainty and drove the development of RANS turbulence modeling [35], it turns out that deep learning can effectively mine the deep information from the flow field data (obtained from expensive CFD calculations) and finish the predicting of the entire flow field in milliseconds. In particular, the convolutional neural network (CNN) is widely used in the field of aerodynamic design and optimization to reduce the complexity of the deep learning network, through strategies of the local receptive field, weight sharing, and down-sampling, as it is invariant to the degree of variation in the form of translation, rotation, and scaling. [PERSON] et al. [36] trained two types of CNN architectures to predict the lift coefficient of a given airfoil shape in different flow conditions, the results demonstrate that their CNN model has good accuracy and could learn faster than the multi-layer perceptron (MLP). [PERSON] et al. presented another CNN-based model to learn the airfoil lift coefficient calculated from CFD results, where a \"feature-enhanced-image\" data preprocessing method was developed to achieve higher prediction accuracy [37]. [PERSON] et al. [38] proposed a CNN-based data-driven approach to quickly predict the pressure distribution around the airfoils with a mean square error of less than 2%. [PERSON] et al. [39] used CNN to establish an unsteady data-driven ROM for predicting the velocity field around an airfoil, where a mapping function was constructed between the temporal evolution of the pressure and velocity. [PERSON] et al. [40]adopted long-term memory (LSTM) network to build an unsteady aerodynamic ROM, as it could accurately capture the dynamic characteristics of aerodynamic systems under various flow and structure parameters. [PERSON] et al. [41] built a CNN model combined with the generative adversarial network (GAN) to achieve the mapping from parameterized airfoils to corresponding transonic flow field under fixed operating conditions. [PERSON] et al. [42] developed a data-driven model to obtain real-time predictions of 2D and 3D flows with good efficiency and generalization property. This work aims to propose a novel approach to achieve accurate and rapid flow field inference for airfoil design optimization based on deep learning, in a less computationally demanding manner instead of expensive CFD simulation tools. In this paper, a CNN-based data-driven method is proposed for fast prediction of the steady flow field around NACA (National Advisory Committee for Aeronautics) 0012 airfoil under different far-field velocities for a series of geometric parameters. The morphing of the airfoil profile is controlled by changing the maximum camber and its position along the chord, while keeping maximum thickness at a constant value. The model establishes a mapping function between the geometric profile and corresponding external flow fields, namely pressure, and velocity. Specifically, the proposed model consists of a CNN and a deconvolutional neural network (DCNN), referred to as the CNN-DCNN model. Acting as an encoder, CNN mines the intrinsic features of the physical field [43] into a lower dimensional space, while DCNN decodes and reconstructs the full-dimensioned physical field.