Incorporating Riemannian Geometric Features for Learning Coefficient of
  Pressure Distributions on Airplane Wings
Liwei Hu Wenyong Wang Yu Xiang Stefan Sommer
The aerodynamic coefficients of aircrafts are significantly impacted by its
geometry, especially when the angle of attack (AoA) is large. In the field of
aerodynamics, traditional polynomial-based parameterization uses as few
parameters as possible to describe the geometry of an airfoil. However, because
the 3D geometry of a wing is more complicated than the 2D airfoil,
polynomial-based parameterizations have difficulty in accurately representing
the entire shape of a wing in 3D space. Existing deep learning-based methods
can extract massive latent neural representations for the shape of 2D airfoils
or 2D slices of wings. Recent studies highlight that directly taking geometric
features as inputs to the neural networks can improve the accuracy of predicted
aerodynamic coefficients. Motivated by geometry theory, we propose to
incorporate Riemannian geometric features for learning Coefficient of Pressure
(CP) distributions on wing surfaces. Our method calculates geometric features
(Riemannian metric, connection, and curvature) and further inputs the geometric
features, coordinates and flight conditions into a deep learning model to
predict the CP distribution. Experimental results show that our method,
compared to state-of-the-art Deep Attention Network (DAN), reduces the
predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11
aircraft test set.