Aerodynamic shape optimization using graph variational autoencoders and genetic algorithms

The use of machine learning in aerodynamic shape optimization problems has significantly increased in recent years. While existing deep learning techniques enable efficient design space exploration on data with an underlying Euclidean or grid-like structure, the direct optimization of non-parametric 3D geometries is still limited. In this article, we propose a geometric deep learning model that generates triangled-based meshed surfaces through the use of a graph variational autoencoder that learns the latent representations of a non-parametric 3D dataset. Once this framework is trained to embed all the input meshes in a properly distributed latent space, its exploration is managed by a genetic algorithm. In this regard, the NSGA-II is the agent in charge of sampling geometries that combine topology and aerodynamic features of the initial ones. Furthermore, in each iteration, it evaluates their aerodynamic performance with CFD in order to guide the optimization process and find the most effective region of the latent space. As a result, those solutions that maximize aerodynamic performance are provided through a Pareto front. The application to a case study and a real-world application is introduced aiming to validate the proposed approach.