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Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

Spectral graph convolutional neural networks (GCNNs) have been producing encouraging results in graph classification tasks. However, most spectral GCNNs utilize fixed graphs when aggregating node features, while omitting edge feature…

Deep learning has shown remarkable results on Euclidean data (e.g. audio, images, text) however this type of data is limited in the amount of relational information it can hold. In mathematics we can model more general relational data in a…

Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…

There have been recent efforts to learn more meaningful representations via fixed length codewords from mesh data, since a mesh serves as a complete model of underlying 3D shape compared to a point cloud. However, the mesh connectivity…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…

The application of deep learning to 3D point clouds is challenging due to its lack of order. Inspired by the point embeddings of PointNet and the edge embeddings of DGCNNs, we propose three improvements to the task of point cloud analysis.…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…

Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use…

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features…

Unstructured point clouds with varying sizes are increasingly acquired in a variety of environments through laser triangulation or Light Detection and Ranging (LiDAR). Predicting a scalar response based on unstructured point clouds is a…

We introduce UV-Net, a novel neural network architecture and representation designed to operate directly on Boundary representation (B-rep) data from 3D CAD models. The B-rep format is widely used in the design, simulation and manufacturing…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Most algorithms that rely on deep learning-based approaches to generate 3D point sets can only produce clouds containing fixed number of points. Furthermore, they typically require large networks parameterized by many weights, which makes…

Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep AutoEncoder (AE) network with…

Existing deep learning algorithms for point cloud analysis mainly concern discovering semantic patterns from global configuration of local geometries in a supervised learning manner. However, very few explore geometric properties revealing…