Nonlinear Aerodynamic Shape Reduction Using Variational Autoencoder and Model-Agnostic Meta-Learning

Generating realistic airfoil shapes from any random parameter combinations is highly desirable for a parameterization method to improve the performance of aerodynamic shape optimization frameworks. Data-driven techniques with generative capabilities, such as Variational Autoencoders (VAE), stand as a good alternative for that purpose, as they utilize the prior airfoil knowledge to learn the properties of a valid airfoil shape, yet can still predict innovative geometries. However, direct training of these complex models is not generally possible using the existing airfoil datasets due to the limited and imbalanced nature of the available samples, leading to the prediction of non-smooth airfoil shapes. To address this limitation, a training strategy is proposed in this study, involving pretraining using a Model-Agnostic Meta-Learning (MAML) approach, followed by fine-tuning with the UIUC airfoil dataset. The trained VAE model can predict smooth airfoil shapes, and the smoothness improves with the number of samples used during the pretraining stage. The findings suggest that six total parameters, three for thickness and three for camber reconstruction, are sufficient to represent the UIUC dataset accurately. The trained model is also employed in an inverse shape optimization example, demonstrating the potential and the limitations of the proposed parametrization method in an aerodynamic shape optimization framework.