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. We propose a deep generative model, B\'ezier-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. We use the airfoil design as an example to demonstrate the idea and analyze B\'ezier-GAN's representation capacity and compactness. Results show that B\'ezier-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 to state-of-the-art parameterization methods.

本文提出了一种深度生成模型Bezier-GAN来压缩参数化飞行器设计，从而以更紧凑的方式获得充分的可表示容量，同时保持充分的表示容量。在空气动力学设计的示例中，通过分析Bezier-GAN的表示能力和紧凑性，结果表明该方法在范围广泛的翼型中学习光滑、逼真的形状表示，并与最先进的参数化方法相比，至少将优化收敛加速两倍。

利用贝塞尔生成对抗网络进行翼型参数化设计和优化