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.
Code (0)
등록된 구현이 없습니다.
Tasks
3D geometryDeep AttentionMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is class…
EEG-Based User Reaction Time Estimation Using Riemannian Geometry Features
Riemannian geometry has been successfully used in many brain-computer interface (BCI) classification problems and demonstrated superior performance. In this paper, for the first time, it is applied to BCI regression prob…
Brain Computer InterfaceEEGElectroencephalogram (EEG)regressionNon-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity tha…
Dimensionality ReductionRiemann$^2$: Learning Riemannian Submanifolds from Riemannian Data
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, …
Motion SynthesisRiemannian Geometric-based Meta Learning
Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, the…
Few-Shot LearningMeta-Learning