# Aerodynamic Analyses of Airfoils Using Machine Learning as an Alternative to RANS Simulation
###### Abstract
A RANS-based CFD simulation was performed at selected Mach numbers and attack angles to forecast the pressure fields of a known airfoil, the results of which were then provided to a neural network architecture that was trained to predict pressure fields around unknown airfoil shapes. They achieved an almost 88% rate of accuracy for unseen airfoils and accelerated the speed of the simulation process using much cheaper computational resources. [PERSON] et al. [3] trained a shared encoding and decoding approximation that was based on a CNN model to envisage RANS flow patterns around different airfoil shapes in varying flow settings. Similar to the previous cases, they used the flow Reynolds number and attack angles of the airfoils, along with the signed distance function (SDF) of the airfoil profile, as input parameters for the proposed training algorithm. [PERSON] et al. [4] built a two-layer ConvNet for nonlinear problems with large scales to forecast their aerodynamic coefficients. They claimed that their proposed method was better than existing surrogate models and had the ability to enhance the accuracy of predicting the drag and lift coefficients of airfoils. They also compared the performances of ReLU and tanh activation functions in their model and found that ReLU produced a comparatively better performance in terms of the accuracy of the predicted aerodynamic coefficients. [PERSON] et al. [5] presented a comprehensive review of the current advances in data-driven approaches for the study of turbulence problems using RANS equations. The authors pointed out that CNN-based analyses have great potential for use in turbulence modeling problems. [PERSON] et al. [6] worked on another artificial neural network model, which was embedded with the Galilean invariance to solve RANS turbulence models. The authors claimed that their model showed significant improvements in accurate predictions compared to the generic MLP that was not embedded with invariance properties. [PERSON] et al. [7] investigated subsonic attached flows around an airfoil using an artificial neural network model by constructing eddy viscosity mapping. The authors claimed that this model was more efficient than the Spalart-Allmaras model in terms of achieving convergence in fewer iterations. [PERSON] et al. [8] employed a radial basis function neural network as a classifier to monitor corrosion inside industrial pipes and subsequently categorize its findings based on the corrosion type. The scholars trained the network using five inputs and two output neurons with a preset target MSE value of 0.0074. They achieved a very high detection accuracy rate of around 99.45%. [PERSON] et al. [9] worked on an adaptive control technique that was based on a radial basis function neural network (RBFNN). The coefficient of lift of an airfoil was assumed to be the response indicator and the trailing edge flap was assumed to be the actuator. Bycontinuously changing the attack angle of the airfoil and varying the Mach number, this model could completely suppress the buffet load over an airfoil. In their work, [PERSON] et al. [10] presented a methodology that was also built upon RBFNN for monitoring the harmonic amplitudes of observed signals in order to prevent power quality degradation in electronic power distribution systems. This method, according to the authors, provided a better accuracy with fewer sample data in comparison to the other frequently used approaches. In another work, [PERSON] et al. [11] employed the regression model of RBFNN to predict the growth rates of fatigue cracks in the aluminum alloys of an airplane. The network was trained using two inputs and a single output neuron with a preset target MSE of 5 \(\times\) 10\({}^{-11}\). They discovered a good correlation between the experimental and predicted data. [PERSON] et al. [12] developed and compared the performances of two different artificial neural network architectures that used feed-forward and recurrent models to study unsteady aerodynamic features in stretched angles of attack.