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.

中文翻译：

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使用 B\'ezier 生成对抗网络进行翼型设计参数化和优化

由于设计空间的高维度，空气动力学形状的全局优化通常需要大量昂贵的计算流体动力学模拟。解决这个问题的一种方法是通过获得新的表示来减少设计空间维度。这需要一个参数函数，它可以紧凑而充分地描述形状的有用变化。我们提出了一个深度生成模型 B\'ezier-GAN，通过从现有数据库中的形状变化中学习来参数化空气动力学设计。由此产生的新参数化可以通过提高表示紧凑性同时保持足够的表示能力来加速设计优化收敛。我们以翼型设计为例来演示这个想法并分析 B\'ezier-GAN' s 表示能力和紧凑性。结果表明，与最先进的参数化方法相比，B\'ezier-GAN (1) 学习了各种翼型的平滑和逼真的形状表示，并且 (2) 根据经验将优化收敛速度提高了至少两倍。