Related papers: Learning Geometric-Aware Quadrature Rules for Func…

We propose an approach based on Artificial Neural Networks (ANNs) to evaluate geometric constants relevant to the analysis and design of numerical schemes for partial differential equations. These constants play a central role,…

The combination of linear transformations and non-linear activation functions forms the foundation of most modern deep neural networks, enabling them to approximate highly complex functions. This paper explores the introduction of quadratic…

Shape completion, the problem of inferring the complete geometry of an object given a partial point cloud, is an important problem in robotics and computer vision. This paper proposes the Graph Attention Shape Completion Network (GASCN), a…

The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their…

Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named…

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…

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.…

Among 2D convolutional networks on point clouds, point-based approaches consume point clouds of fixed size directly. By analysis of PointNet, a pioneer in introducing deep learning into point sets, we reveal that current point-based methods…

Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…

We propose a practical deep generative approach for lossless point cloud geometry compression, called MSVoxelDNN, and show that it significantly reduces the rate compared to the MPEG G-PCC codec. Our previous work based on autoregressive…

Weight pruning is an effective model compression technique to tackle the challenges of achieving real-time deep neural network (DNN) inference on mobile devices. However, prior pruning schemes have limited application scenarios due to…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep…

Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and…

Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…

Graph Neural Networks (GNNs) have become a popular approach for various applications, ranging from social network analysis to modeling chemical properties of molecules. While GNNs often show remarkable performance on public datasets, they…

Graph neural networks (GNNs) demonstrate a robust capability for representation learning on graphs with complex structures, showcasing superior performance in various applications. The majority of existing GNNs employ a graph convolution…

This work introduces the Nirenberg Neural Network: a numerical approach to the Nirenberg problem of prescribing Gaussian curvature on $S^2$ for metrics that are pointwise conformal to the round metric. Our mesh-free physics-informed neural…

Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…

Owing to the development of research on local aggregation operators, dramatic breakthrough has been made in point cloud analysis models. However, existing local aggregation operators in the current literature fail to attach decent…