# Fast Prediction of Flow Field around Airfoils Based on Deep Convolutional Neural Network
## 1 Introduction  
The aerodynamic performance and safety of airfoil rely on multiple parameters including geometry profile, flight speed, angle of attack (AOA), atmospheric density, and other operating conditions. As parameter study by wind tunnel experiment is prohibitively expensive and time-consuming, a more efficient approach to evaluate the aerodynamic performance is generally required, especially during the design process, so that choices of parameters could be narrowed before physical experiments. Currently, the most typical solution for fast aerodynamic evaluation of is Computational Fluid Dynamics (CFD), when solving Reynolds-averaged Navier-Stokes (RANS) equations, the computational cost of CFD is significantly lower than that of a wind tunnel test at the same scale. However, as optimization metrics of modern aircraft design become more sophisticated, the volume of parameter studies also grows substantially, in which case even RANS becomes too expensive, and an evaluation or prediction method cheaper than CFD is necessary [1; 2; 3]. One important solution for fast aerodynamic evaluation, such as flow fields, pressure distribution coefficient, lift coefficient, and drag coefficient, is to constitute surrogate models. The basic idea is to run CFD calculations on only a few sampled geometry profiles, train and construct a surrogate model through the CFD database, then use the surrogate model instead of explicit CFD for further calculations of airfoil geometries outside the sampled database. As surrogate models avoid the expensive solution of RANS equations, the prediction (calculation) wall time could be greatly reduced, making the search for optimal geometry much more practical under variable flow conditions. Major developments of thesurrogate model coupled with CFD include methods of multi-fidelity, reduced-order model (ROM), and data-driven model [4]. They have been successfully applied to enhance the efficiency of aerodynamic performance evaluation, such as polynomial response surface (PRS) [5], artificial neural network (ANN) [6; 7], radial basis function (RBF) [8], support vector machine (SVM) [9], Kriging model [10; 11; 12], and Gaussian process (GP) [13; 14] regression. Nevertheless, most of the traditional surrogate models are narrowly appropriate for predicting low-dimensional physical quantities such as lift and drag coefficient, and moment coefficient, offering averaged characteristics rather than the complete high-dimensional flow field information. Fast development of machine learning (ML) technology in recent years bring promising breakthroughs for surrogate models to directly address high-dimensional physical fields. [PERSON] et al. [15] and [PERSON] et al. [16] applied the neural network method to generic aircraft to predict aerodynamic coefficients which are modeled as functions of the angle of attack (AOA), Mach number, Reynolds number, and airfoil geometry. [PERSON] et al. [17] conducted a benchmark study on the optimization of aerodynamic shape using POD-based Class-Shape Function Transformation (CST) methods. [PERSON] and [PERSON] developed a Kriging regression surrogate model-based optimization technique to mitigate the deep dynamic stall characteristics of airfoils [18]. [PERSON] et al. [19] replaced the solution of governing partial differential equations with neural networks, which directly reconstruct the mapping between the turbulent eddy viscosity and the mean flow variables. ML or neural network methods aim to establish a non-linear mapping between input parameters and output, saving the otherwise expensive solution of Navier Stokes equations. However, they just mechanically search for pure input-output mapping [20; 21] without exploiting the abundant and intrinsic physical information which exactly concerned designers. Besides, most current ML-based surrogate models are shallow models, they are trained towards only the original function subspace, rather than the whole complex nonlinear function space, lacking generalization ability for data never seen from the training set.