Journal Article

Scalable gradient-enhanced artificial neural networks for airfoil shape design in the subsonic and transonic regimes


M. A. Bouhlel, S. He, and J. R. R. A. Martins


Structural and Multidisciplinary Optimization, 611363–1376, 2020



Airfoil shape design is one of the most fundamental elements in aircraft design. Existing airfoil design tools require at least a few minutes to analyze a new shape and hours to perform shape optimization. To drastically reduce the computational time of both analysis and design optimization, we use machine learning to create a model of a wide range of possible airfoils at a range of flight conditions, making it possible to perform airfoil design optimization in a few seconds. The machine learning consists of gradient-enhanced artificial neural networks where the gradient information is phased in gradually. This new gradient-enhanced artificial neural network approach is trained to model the aerodynamic force coefficients of airfoils in both subsonic and transonic regimes. The aerodynamics is modeled with Reynolds-averaged Navier–Stokes (RANS) based computational fluid dynamics (CFD). The proposed approach outperforms an existing airfoil model that uses a mixture of experts technique combined with a gradient-based Kriging surrogate model. The approach yields to similar airfoil shape optimization solutions than high-fidelity CFD optimization solutions with a difference of 0.01 count and 0.12 count for C d in subsonic and transonic regimes, respectively. Airfoil optimization problems are solved in a few seconds (instead of hours using CFD-based optimization), making the design process much more interactive, as demonstrated in the Webfoil airfoil design optimization tool.