Learning Airfoil Manifolds with Optimal Transport

Qiuyi Chen, Phil Pope, Mark Fuge

Abstract:

The manifold hypothesis forms a pillar of many modern machine learning techniques. Within the context of design, it proposes that valid designs reside on low dimensional manifolds in the high dimensional design spaces. Our previous research—BézierGAN—suggests learning
the low dimensional parameterization of valid airfoil designs can indeed accelerate aerodynamic optimizations. However, it incurs problems such as misalignment, long training time, and the trouble of finding the latent dimensionality. In this work we present the optimal-transport-based sibling of BézierGAN that surpass its predecessor in terms of both manifold approximating precision and learning speed, and provide methodology that helps determine the intrinsic dimension of the design manifold beforehand.