Constraint-Based Parameterization and Disentanglement of Aerodynamic Shapes Using Deep Generative Models

Abstract

Generating parametric shapes with respect to their structural and functional characteristics is a challenging and demanding problem. Conventional parameterization techniques are complex and require manual intervention and multiple cycles to produce plausible shapes, which makes the overall parameterization process extremely sensitive, time- consuming and error-prone. Despite these techniques’ slow and iterative nature, a significant amount of data has been gathered over many years, prompting the community to turn to data-driven techniques like deep generative models for automatic parameterization. However, parameterizing shapes following necessary functional constraints is crucial but notoriously difficult and still needs to be studied. Therefore, we propose a data-driven framework that implicitly learns to generate plausible parametric aerodynamic shapes under specified constraints. We explore and compare several generative models, including generative adversarial networks and variational autoencoders, and systematically evaluate them for generation quality, diversity, and disentanglement aspects. Our framework, including a $\beta $ -VAE model, enables the automatic generation of novel airfoils with watertight boundaries and interactive generation with its distributed and disentangled latent space. Through rigorous evaluation of our method, we demonstrate that the generated distribution closely matches the true distribution, resulting in the generation of highly realistic airfoils. Our method dramatically outperforms the current benchmark in terms of the quality and diversity of generated airfoils and establishes a new benchmark for constraint-based parameterization.