  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.
