Related papers: A Manifold-based Airfoil Geometric-feature Extract…

Accurate and complete aerodynamic data sets are the basis for comprehensive and accurate evaluation of the overall performance of aircraft. However, the sampling cost of full-state aerodynamic data is extremely high, and there are often…

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…

The design of aerodynamic shapes, such as airfoils, has traditionally required significant computational resources and relied on predefined design parameters, which limit the potential for novel shape synthesis. In this work, we introduce a…

Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…

The adaptability of the convolutional neural network (CNN) technique for aerodynamic meta-modeling tasks is probed in this work. The primary objective is to develop suitable CNN architecture for variable flow conditions and object geometry,…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…

Dynamic mode decomposition (DMD) has proven to be a valuable tool for the analysis of complex flow-fields but the application of this technique to flows with moving boundaries is not straightforward. This is due to the difficulty in…

In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning…

We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…

The accurate prediction of flow fields around airfoils is crucial for aerodynamic design and optimisation. Computational Fluid Dynamics (CFD) models are effective but computationally expensive, thus inspiring the development of surrogate…

The current practice of manually processing features for high-dimensional and heterogeneous aviation data is labor-intensive, does not scale well to new problems, and is prone to information loss, affecting the effectiveness and…

Accurate aerodynamic field prediction is crucial for vehicle drag evaluation, but the computational cost of high-fidelity CFD hinders its use in iterative design workflows. While learning-based methods enable fast and scalable inference,…

The precise fusion of computational fluid dynamic (CFD) data, wind tunnel tests data, and flight tests data in aerodynamic area is essential for obtaining comprehensive knowledge of both localized flow structures and global aerodynamic…

We propose a novel 3D spatial representation for data fusion and scene reconstruction. Probabilistic Signed Distance Function (Probabilistic SDF, PSDF) is proposed to depict uncertainties in the 3D space. It is modeled by a joint…

Existing EEG foundation models mainly treat neural signals as generic time series in Euclidean space, ignoring the intrinsic geometric structure of neural dynamics that constrains brain activity to low-dimensional manifolds. This…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

Existing deep learning based methods effectively prompt the performance of aerial scene classification. However, due to the large amount of parameters and computational cost, it is rather difficult to apply these methods to multiple…