# Geometric and Physical Quantities improve E(3) Equivariant Message Passing

@article{Brandstetter2022GeometricAP, title={Geometric and Physical Quantities improve E(3) Equivariant Message Passing}, author={Johannes Brandstetter and Rob Hesselink and Elise van der Pol and Erik J. Bekkers and Max Welling}, journal={ArXiv}, year={2022}, volume={abs/2110.02905} }

Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E( 3 ) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant graph networks, such that node and edge attributes are not restricted to invariant scalars, but can contain covariant information, such as vectors or tensors. This model, composed of steerable MLPs, is able to incorporate geometric and physical information…

## 37 Citations

### SE(3) Equivariant Graph Neural Networks with Complete Local Frames

- Computer ScienceICML
- 2022

Inspired by differential geometry and physics, equivariant local complete frames are introduced to graph neural networks, such that tensor information at given orders can be projected onto the frames, and the method is computationally efficient.

### MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields

- Computer ScienceArXiv
- 2022

This work introduces MACE, a new equivariant MPNN model that uses higher body order messages and shows that using four-body messages reduces the required number of message passing iterations to just two, resulting in a fast and highly parallelizable model, reaching or exceeding state-of-the-art accuracy on the rMD17, 3BPA, and AcAc benchmark tasks.

### Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics

- Computer ScienceArXiv
- 2022

Allegro is introduced, a strictly local equivariant deep learning interatomic potential that simultaneously exhibits excellent accuracy and scalability of parallel computation and remarkable generalization to out-of-distribution data.

### Steerable Partial Differential Operators for Equivariant Neural Networks

- Computer ScienceICLR
- 2022

This work derives a G-steerability constraint that completely characterizes when a PDO between feature vector fields is equivariant, for arbitrary symmetry groups G, and develops a framework forEquivariant maps based on Schwartz distributions that unifies classical convolutions and differential operators and gives insight about the relation between the two.

### Hierarchical Learning in Euclidean Neural Networks

- Computer ScienceArXiv
- 2022

This work examines the role of higher order (non-scalar) features in Euclidean Neural Networks (e3nn) and finds a natural hierarchy of features by l, reminiscent of a multipole expansion, to ultimately inform design principles and choices of domain applications for e3nn networks.

### Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs

- Computer ScienceArXiv
- 2022

To better adapt Transformers to 3D graphs, a novel equivariant graph attention is proposed, which considers both content and geometric information such as relative position contained in irreps features.

### Learning Symmetric Embeddings for Equivariant World Models

- Computer ScienceICML
- 2022

This work proposes learning symmetric embedding networks (SENs) that encode an input space that transforms in a known manner under these oper-ations, and demonstrates that SENs facilitate the application of equivariant networks to data with complex symmetry representations.

### Geometrically Equivariant Graph Neural Networks: A Survey

- Computer ScienceArXiv
- 2022

This work analyzes and classify existing methods into three groups regarding how the message passing and aggregation in GNNs are represented, and summarizes the benchmarks as well as the related datasets to facilitate later researches for methodology development and experimental evaluation.

### ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks

- Computer Science
- 2022

ACMP provides a deep model of GNNs circumventing the common GNN problem of oversmoothing and achieves state of the art performance for real-world node classiﬁcation tasks on both homophilic and heterophilic datasets.

### e3nn: Euclidean Neural Networks

- Computer ScienceArXiv
- 2022

We present e3nn , a generalized framework for creating E(3) equivariant trainable functions, also known as Euclidean neural networks. e3nn nat-urally operates on geometry and geometric tensors that…

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