# Relaxing Continuous Constraints of Equivariant Graph Neural Networks for Physical Dynamics Learning

arXiv: https://arxiv.org/abs/2406.16295 · HTML: https://mlsanity.com/paper/2406.16295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 54 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 29 of 29)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Transformer Networks for Trajectory Forecasting](https://mlsanity.com/paper/2003.08111/) (2020)
- [LieTransformer: Equivariant self-attention for Lie Groups](https://mlsanity.com/paper/2012.10885/) (2020)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [Multi-Modal Trajectory Prediction of Surrounding Vehicles with Maneuver based LSTMs](https://mlsanity.com/paper/1805.05499/) (2018)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Equivariant Flows: sampling configurations for multi-body systems with symmetric energies](https://mlsanity.com/paper/1910.00753/) (2019)
- [SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases](https://mlsanity.com/paper/2308.13212/) (2023)
- [Generalizing Graph ODE for Learning Complex System Dynamics across Environments](https://mlsanity.com/paper/2307.04287/) (2023)
- [Modelling High-Order Social Relations for Item Recommendation](https://mlsanity.com/paper/2003.10149/) (2020)
- [Hierarchical Graph Capsule Network](https://mlsanity.com/paper/2012.08734/) (2020)
- [Spatial Attention Kinetic Networks with E(n)-Equivariance](https://mlsanity.com/paper/2301.08893/) (2023)
- [Weakly Supervised Anomaly Detection via Knowledge-Data Alignment](https://mlsanity.com/paper/2402.03785/) (2024)
- [Human Mobility Modeling During the COVID-19 Pandemic via Deep Graph Diffusion Infomax](https://mlsanity.com/paper/2212.05707/) (2022)
- [Deep Reinforcement Learning for Modelling Protein Complexes](https://mlsanity.com/paper/2405.02299/) (2024)

## Built on by (most cited first, 1 of 1)

- [Relaxed Equivariance via Multitask Learning](https://mlsanity.com/paper/2410.17878/) (2024)

## Abstract (arXiv)

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various scientific and engineering applications, the symmetries of dynamics are frequently discrete due to the boundary conditions. Thus, existing GNNs either overlook necessary symmetry, resulting in suboptimal representation ability, or impose excessive equivariance, which fails to generalize to unobserved symmetric dynamics. In this work, we propose a general Discrete Equivariant Graph Neural Network (DEGNN) that guarantees equivariance to a given discrete point group. Specifically, we show that such discrete equivariant message passing could be constructed by transforming geometric features into permutation-invariant embeddings. Through relaxing continuous equivariant constraints, DEGNN can employ more geometric feature combinations to approximate unobserved physical object interaction functions. Two implementation approaches of DEGNN are proposed based on ranking or pooling permutation-invariant functions. We apply DEGNN to various physical dynamics, ranging from particle, molecular, crowd to vehicle dynamics. In twenty scenarios, DEGNN significantly outperforms existing state-of-the-art approaches. Moreover, we show that DEGNN is data efficient, learning with less data, and can generalize across scenarios such as unobserved orientation.