# Aerodynamic Analyses of Airfoils Using Machine Learning as an Alternative to RANS Simulation
###### Abstract
The training of the NNs was conducted using experimental data. They concluded that the recurrent neural network was favorable for modeling unsteady flows. [PERSON] et al. [13] proposed the coupling of a physical solver and a CNN to speed up the convergence of RANS simulations. The CNN model was fed with the initial CFD simulation results from the warm-up stage as inputs from the physical solver and then, after the application of the model, the predicted results from the CNN were fed back into the physical solver for final refinement. In this way, the convergence constraints were met about 7.4 times faster for steady laminar flows, as well as turbulent flows. [PERSON] et al. [14] worked on three different artificial neural network models, which included a CNN model, a Unet model and a Resnet model, for the identification of vortex boundary layers in wake regions. They found Unet to be better for the subject task in terms of accuracy. [PERSON] et al. [15] implemented an unsteady aerodynamic network that was built upon long- and short-term memory to predict aerodynamic and aeroelastic responses. The parameters, such as pitching angle and plunging displacement of the selected airfoil and the flow Mach number, were fed into model as inputs to obtain the lift and pitch moment coefficients as outputs. [PERSON] et al. [16] worked on a recurrent neural network for the identification of nonlinear aerodynamic parameters. Unsteady aerodynamic parameters that were obtained using CFD were used, along with the excitation signals, to train the network to predict the aerodynamic forces that were produced by composite sinusoidal motion. Their model was able to precisely recognize the large-amplitude nonlinear unsteady aerodynamic forces of airfoils. [PERSON] et al. [17] developed a framework that comprised full-field inversions to model the source term in SA turbulence using a neural network. The framework was entrenched with a RANS solver to enhance the utility of the SA model in predicting the large adverse pressure deviations in flows around airfoils, both before and after the stall occurred. Similar to the other machine learning approaches, researchers have also extensively studied the applications of back-propagation neural networks (BPNNs). [PERSON] et al. [18] applied a back-propagation neural network that was based on an ANN technique in their study to anticipate domestic energy usage roughly one hour before the electric supply was even provided to the inhabitants. They were able to predict this usage for one complete week with a mean error of 1.5%. In another study, [PERSON] et al. [19] used a BPNN to project annual rainfall in different areas. [PERSON] et al. [20] utilized a BPNN, along with an RBFNN, to curtail hydrogen usage in the fuel cell of an electric vehicle by estimating its speed. The application of the BPNN in their study helped them to correctly estimate the speed of the vehicle. [PERSON] et al. [21] employed a BPNN to predict the ratio of lift to drag coefficients at different angles of attack. They trained their model using three input parameters, namely the tip chord, winglet height and cant angle, and one output. The ratio of lift to drag coefficients was estimated with a mean squared error of 4.96 \(\times\) 10\({}^{-8}\). Following this survey of the literature, the possibility of the application of supervised machine learning techniques in the field of aerodynamics was further explored in this study. Since much less research has been conducted on the application of back-propagation neural networks in aerodynamics, we trained a BPNN model using an aerodynamic dataset that contained varying operating conditions as the input data and the corresponding aerodynamic coefficients as the target data. The basic aim of the present study was to devise an artificial neural network architecture that can predict the most important aerodynamic characteristics, i.e., the coefficient of drag (\(\mathrm{C_{D}}\)) and coefficient of lift (\(\mathrm{C_{L}}\)), that are produced by airfoils under different aerodynamic conditions.