Physically Interpretable Feature Learning and Inverse Design of Supercritical Airfoils

TL;DR

This paper introduces a physically interpretable feature learning method using variational autoencoders for fluid dynamics, enabling inverse design of supercritical airfoils based on physical features rather than pressure data.

Contribution

It develops a novel feature learning algorithm that assigns physical meaning to latent variables and applies it to inverse design of supercritical airfoils.

Findings

The algorithm accurately reconstructs pressure distributions with physical interpretability.

It enables manipulation of pressure features in airfoil design without affecting other features.

The method outperforms other variational autoencoders in interpretability and accuracy.

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 is able to assign physical features to some latent variables of the variational autoencoder. In addition, 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 pressure distributions. The reconstruction accuracy and physical interpretability are also compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils, which enables the generation of airfoil geometries based on physical features rather than the complete pressure distributions. It also demonstrates the ability to manipulate certain pressure distribution features of the airfoil without changing the others.