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

arXiv: https://arxiv.org/abs/2401.09452 · HTML: https://mlsanity.com/paper/2401.09452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 12 of 12)

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- [Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization](https://mlsanity.com/paper/2101.04757/) (2021)
- [Simultaneous Alignment and Surface Regression Using Hybrid 2D-3D Networks for 3D Coherent Layer Segmentation of Retinal OCT Images with Full and Sparse Annotations](https://mlsanity.com/paper/2312.01726/) (2023)
- [Aerodynamic Data Predictions Based on Multi-task Learning](https://mlsanity.com/paper/2010.09475/) (2020)
- [A Manifold-based Airfoil Geometric-feature Extraction and Discrepant Data Fusion Learning Method](https://mlsanity.com/paper/2206.12254/) (2022)
- [Empirical study of the modulus as activation function in computer vision applications](https://mlsanity.com/paper/2301.05993/) (2023)

## Abstract (arXiv)

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.