Related papers: E(3)-Equivariant Mesh Neural Networks

The ability of convolutional neural networks (CNNs) to recognize objects regardless of their position in the image is due to the translation-equivariance of the convolutional operation. Group-equivariant CNNs transfer this equivariance to…

Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

Deep learning-based models have recently outperformed state-of-the-art seasonal forecasting models, such as for predicting El Ni\~no-Southern Oscillation (ENSO). However, current deep learning models are based on convolutional neural…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

During the last years, many advances have been made in tasks like3D model retrieval, 3D model classification, and 3D model segmentation.The typical 3D representations such as point clouds, voxels, and poly-gon meshes are mostly suitable for…

Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher-order…

This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary…

Material characterization using electron micrographs is a crucial but challenging task with applications in various fields, such as semiconductors, quantum materials, batteries, etc. The challenges in categorizing electron micrographs…

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…

Although numerical models provide accurate solutions for ice sheet dynamics based on physics laws, they accompany intensified computational demands to solve partial differential equations. In recent years, convolutional neural networks…

Equivariant Graph Neural Networks (EGNNs) have demonstrated significant success in modeling microscale systems, including those in chemistry, biology and materials science. However, EGNNs face substantial computational challenges due to the…

Mesh-based graph neural networks (GNNs) have become effective surrogates for PDE simulations, yet their deep message passing incurs high cost and over-smoothing on large, long-range meshes; hierarchical GNNs shorten propagation paths but…

Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space.…

It is well established that graph neural networks (GNNs) can be interpreted and designed from the perspective of optimization objective. With this clear optimization objective, the deduced GNNs architecture has sound theoretical foundation,…

In this paper, we introduce group convolutional neural networks (GCNNs) equivariant to color variation. GCNNs have been designed for a variety of geometric transformations from 2D and 3D rotation groups, to semi-groups such as scale.…

Point cloud normal estimation is a fundamental task in 3D geometry processing. While recent learning-based methods achieve notable advancements in normal prediction, they often overlook the critical aspect of equivariance. This results in…

Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research. Recent works on mesh processing have concentrated on various kinds of natural symmetries, including translations, rotations, scaling, node…