Airfoil Design Parameterization and Optimization Using Bézier Generative Adversarial Networks

Global optimization of aerodynamic shapes usually requires a large number of expensive computational fluid dynamics simulations because of the high dimensionality of the design space. One approach to combat this problem is to reduce the design space dimension by obtaining a new representation. This requires a parametric function that compactly and sufficiently describes useful variation in shapes. This paper proposes a deep generative model, Bézier-GAN, to parameterize aerodynamic designs by learning from shape variations in an existing database. The resulted new parameterization can accelerate design optimization convergence by improving the representation compactness while maintaining sufficient representation capacity. The airfoil design is used as an example to demonstrate the idea and analyze Bézier-GAN's representation capacity and compactness. Results show that Bézier-GAN both 1) learns smooth and realistic shape representations for a wide range of airfoils and 2) empirically accelerates optimization convergence by at least two times compared with state-of-the-art parameterization methods.