Related papers: On the Completeness of Invariant Geometric Deep Le…

The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes,…

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does…

Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial…

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes…

Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called…

Quadratic programming (QP) is the most widely applied category of problems in nonlinear programming. Many applications require real-time/fast solutions, though not necessarily with high precision. Existing methods either involve matrix…

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and…

The $k$-Weisfeiler-Leman ($k$-WL) graph isomorphism test hierarchy is a common method for assessing the expressive power of graph neural networks (GNNs). Recently, GNNs whose expressive power is equivalent to the $2$-WL test were proven to…

Graph neural networks (GNNs) are among the most powerful tools in deep learning. They routinely solve complex problems on unstructured networks, such as node classification, graph classification, or link prediction, with high accuracy.…

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…

We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e.,lines, circles, and B-splines). Accordingly, our deep neural…

This work presents FG-Net, a general deep learning framework for large-scale point clouds understanding without voxelizations, which achieves accurate and real-time performance with a single NVIDIA GTX 1080 GPU. First, a novel noise and…

Deep Convolutional Neural Networks (DCNNs) have demonstrated impressive robustness to recognize objects under transformations (eg. blur or noise) when these transformations are included in the training set. A hypothesis to explain such…

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience…

The graph neural network (GNN) has been a powerful deep-learning tool in chemistry domain, due to its close connection with molecular graphs. Most GNN models collect and update atom and molecule features from the fed atom (and, in some…

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…