Learning with Geometry: Including Riemannian Geometric Features in Coefficient of Pressure Prediction on Aircraft Wings

We propose to incorporate Riemannian geometric features from the geometry of aircraft wing surfaces in the prediction of coefficient of pressure (CP) on the aircraft wing. Contrary to existing approaches that treat the wing surface as a flat object, we represent the wing as a piecewise smooth manifold and calculate a set of Riemannian geometric features (Riemannian metric, connection, and curvature) over points of the wing. Combining these features in neighborhoods of points on the wing with coordinates and flight conditions gives inputs to a deep learning model that predicts CP distributions. Experimental results show that the method with incorporation of Riemannian geometric features, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 15.00% for the DLR-F11 aircraft test set.