  A machine learning method was applied to solve an inverse airfoil design
problem. A conditional VAE-WGAN-gp model, which couples the conditional
variational autoencoder (VAE) and Wasserstein generative adversarial network
with gradient penalty (WGAN-gp), is proposed for an airfoil generation method,
and then it is compared with the WGAN-gp and VAE models. The VAEGAN model
couples the VAE and GAN models, which enables feature extraction in the GAN
models. In airfoil generation tasks, to generate airfoil shapes that satisfy
lift coefficient requirements, it is known that VAE outperforms WGAN-gp with
respect to the accuracy of the reproduction of the lift coefficient, whereas
GAN outperforms VAE with respect to the smoothness and variations of generated
shapes. In this study, VAE-WGAN-gp demonstrated a good performance in all three
aspects. Latent distribution was also studied to compare the feature extraction
ability of the proposed method.
