Physically Interpretable Feature Learning of Supercritical Airfoils Based on Variational Autoencoders

Abstract

Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and interpretability of machine learning algorithms. With the increasing application of machine learning in fluid dynamics studies, the need for physically explainable models continues to grow. This paper proposes a feature learning algorithm based on variational autoencoders, which can assign physical features to some latent variables of the variational autoencoder. It is theoretically proved that the remaining latent variables are independent of the physical features. The proposed algorithm is trained to include shock wave features in its latent variables for the reconstruction of supercritical wall Mach number distributions. The reconstruction accuracy and disentanglement are compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils. The proposed algorithm demonstrates the ability to manipulate certain physical features of an airfoil without changing the others, as well as the ability to generate different airfoils with the same physical features by sampling the disentangled latent variables.