# Learning Physical Dynamics with Subequivariant Graph Neural Networks

arXiv: https://arxiv.org/abs/2210.06876 · HTML: https://mlsanity.com/paper/2210.06876/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 30 of 34)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [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)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [ThreeDWorld: A Platform for Interactive Multi-Modal Physical Simulation](https://mlsanity.com/paper/2007.04954/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Learning to Poke by Poking: Experiential Learning of Intuitive Physics](https://mlsanity.com/paper/1606.07419/) (2016)
- [Physion: Evaluating Physical Prediction from Vision in Humans and Machines](https://mlsanity.com/paper/2106.08261/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Learning Physical Intuition of Block Towers by Example](https://mlsanity.com/paper/1603.01312/) (2016)
- [Grounding Physical Concepts of Objects and Events Through Dynamic Visual Reasoning](https://mlsanity.com/paper/2103.16564/) (2021)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [ComPhy: Compositional Physical Reasoning of Objects and Events from Videos](https://mlsanity.com/paper/2205.01089/) (2022)
- [Geometrically Equivariant Graph Neural Networks: A Survey](https://mlsanity.com/paper/2202.07230/) (2022)
- [Visual Grounding of Learned Physical Models](https://mlsanity.com/paper/2004.13664/) (2020)
- [DiffSkill: Skill Abstraction from Differentiable Physics for Deformable Object Manipulations with Tools](https://mlsanity.com/paper/2203.17275/) (2022)
- [Autobahn: Automorphism-based Graph Neural Nets](https://mlsanity.com/paper/2103.01710/) (2021)
- [Natural Graph Networks](https://mlsanity.com/paper/2007.08349/) (2020)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)

## Built on by (most cited first, 30 of 39)

- [Towards Understanding the Generalization of Graph Neural Networks](https://mlsanity.com/paper/2305.08048/) (2023)
- [Equivariant Graph Neural Operator for Modeling 3D Dynamics](https://mlsanity.com/paper/2401.11037/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases](https://mlsanity.com/paper/2308.13212/) (2023)
- [Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?](https://mlsanity.com/paper/2410.11443/) (2024)
- [Geometry-Complete Perceptron Networks for 3D Molecular Graphs](https://mlsanity.com/paper/2211.02504/) (2022)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Subequivariant Graph Reinforcement Learning in 3D Environments](https://mlsanity.com/paper/2305.18951/) (2023)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Understanding Physical Dynamics with Counterfactual World Modeling](https://mlsanity.com/paper/2312.06721/) (2023)
- [Benchmarks for Physical Reasoning AI](https://mlsanity.com/paper/2312.10728/) (2023)
- [Latent Intuitive Physics: Learning to Transfer Hidden Physics from A 3D Video](https://mlsanity.com/paper/2406.12769/) (2024)
- [EqNIO: Subequivariant Neural Inertial Odometry](https://mlsanity.com/paper/2408.06321/) (2024)
- [Latent Field Discovery In Interacting Dynamical Systems With Neural Fields](https://mlsanity.com/paper/2310.20679/) (2023)
- [PGODE: Towards High-quality System Dynamics Modeling](https://mlsanity.com/paper/2311.06554/) (2023)
- [Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learning](https://mlsanity.com/paper/2506.19482/) (2025)
- [A Neural Material Point Method for Particle-based Emulation](https://mlsanity.com/paper/2408.15753/) (2024)
- [Integrating Physics and Topology in Neural Networks for Learning Rigid Body Dynamics](https://mlsanity.com/paper/2411.11467/) (2024)
- [DEL: Discrete Element Learner for Learning 3D Particle Dynamics with Neural Rendering](https://mlsanity.com/paper/2410.08983/) (2024)
- [Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction](https://mlsanity.com/paper/2412.20962/) (2024)
- [Object Dynamics Modeling with Hierarchical Point Cloud-based Representations](https://mlsanity.com/paper/2404.06044/) (2024)
- [Foundations and Frontiers of Graph Learning Theory](https://mlsanity.com/paper/2407.03125/) (2024)
- [Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systems](https://mlsanity.com/paper/2501.07373/) (2025)
- [Subequivariant Reinforcement Learning Framework for Coordinated Motion Control](https://mlsanity.com/paper/2403.15100/) (2024)
- [Subequivariant Reinforcement Learning in 3D Multi-Entity Physical Environments](https://mlsanity.com/paper/2407.12505/) (2024)
- [PAINET: A Principled Efficient Transformer for 3D Dynamics Modeling](https://mlsanity.com/paper/2510.04233/) (2025)
- [Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?](https://mlsanity.com/paper/2307.08226/) (2023)
- [MBDS: A Multi-Body Dynamics Simulation Dataset for Graph Networks Simulators](https://mlsanity.com/paper/2410.03107/) (2024)
- [Neural Force Field: Few-shot Learning of Generalized Physical Reasoning](https://mlsanity.com/paper/2502.08987/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization and should be incorporated into the model design. Existing simulators either consider insufficient symmetry, or enforce excessive equivariance in practice when symmetry is partially broken by gravity. 2) Objects in the physical world possess diverse shapes, sizes, and properties, which should be appropriately processed by the model. To tackle these difficulties, we propose a novel backbone, Subequivariant Graph Neural Network, which 1) relaxes equivariance to subequivariance by considering external fields like gravity, where the universal approximation ability holds theoretically; 2) introduces a new subequivariant object-aware message passing for learning physical interactions between multiple objects of various shapes in the particle-based representation; 3) operates in a hierarchical fashion, allowing for modeling long-range and complex interactions. Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall compared with state-of-the-art GNN simulators, while exhibiting strong generalization and data efficiency.