Related papers: E3x: $\mathrm{E}(3)$-Equivariant Deep Learning Mad…
Convolutional networks are successful, but they have recently been outperformed by new neural networks that are equivariant under rotations and translations. These new networks work better because they do not struggle with learning each…
Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…
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…
Mesh-based 3D static analysis methods have recently emerged as efficient alternatives to traditional computational numerical solvers, significantly reducing computational costs and runtime for various physics-based analyses. However, these…
Spherical convolutional networks have been introduced recently as tools to learn powerful feature representations of 3D shapes. Spherical CNNs are equivariant to 3D rotations making them ideally suited to applications where 3D data may be…
3D reassembly is a fundamental geometric problem, and in recent years it has increasingly been challenged by deep learning methods rather than classical optimization. While learning approaches have shown promising results, most still rely…
This article deals with approximating steady-state particle-resolved fluid flow around a fixed particle of interest under the influence of randomly distributed stationary particles in a dispersed multiphase setup using Convolutional Neural…
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…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
Integrating a notion of symmetry into point cloud neural networks is a provably effective way to improve their generalization capability. Of particular interest are $E(3)$ equivariant point cloud networks where Euclidean transformations…
Convolutional Neural Networks (CNNs) traditionally encode translation equivariance via the convolution operation. Generalization to other transformations has recently received attraction to encode the knowledge of the data geometry in group…
Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of…
In silico prediction of the ligand binding pose to a given protein target is a crucial but challenging task in drug discovery. This work focuses on blind flexible selfdocking, where we aim to predict the positions, orientations and…
Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…
We contribute to the vastly growing field of machine learning for engineering systems by demonstrating that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models than their non-equivariant…
Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue.…
Euclidean E(3) equivariant neural networks that employ scalar fields on position-orientation space M(3) have been effectively applied to tasks such as predicting molecular dynamics and properties. To perform equivariant convolutional-like…
Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…
In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…
Establishing correspondences between 3D shapes is a fundamental task in 3D Computer Vision, typically addressed by matching local descriptors. Recently, a few attempts at applying the deep learning paradigm to the task have shown promising…