# Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learning

arXiv: https://arxiv.org/abs/2412.01297 · HTML: https://mlsanity.com/paper/2412.01297/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 2 Dec 2024.

## Builds on (most cited first, 28 of 28)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Symmetry Considerations for Learning Task Symmetric Robot Policies](https://mlsanity.com/paper/2403.04359/) (2024)
- [Leveraging Symmetry in RL-based Legged Locomotion Control](https://mlsanity.com/paper/2403.17320/) (2024)
- [GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning with End-to-End Learning](https://mlsanity.com/paper/2002.11807/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2212.00893/) (2022)
- [Legged Robot State Estimation using Invariant Kalman Filtering and Learned Contact Events](https://mlsanity.com/paper/2106.15713/) (2021)
- [Morphological Symmetries in Robotics](https://mlsanity.com/paper/2402.15552/) (2024)
- [Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control](https://mlsanity.com/paper/2401.09520/) (2024)
- [On discrete symmetries of robotics systems: A group-theoretic and data-driven analysis](https://mlsanity.com/paper/2302.10433/) (2023)
- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
- [MAGIC-VFM: Meta-learning Adaptation for Ground Interaction Control with Visual Foundation Models](https://mlsanity.com/paper/2407.12304/) (2024)
- [MI-HGNN: Morphology-Informed Heterogeneous Graph Neural Network for Legged Robot Contact Perception](https://mlsanity.com/paper/2409.11146/) (2024)
- [Learning Robot Structure and Motion Embeddings using Graph Neural Networks](https://mlsanity.com/paper/2109.07543/) (2021)
- [Hierarchical Meta-learning-based Adaptive Controller](https://mlsanity.com/paper/2311.12367/) (2023)

## Built on by (most cited first, 5 of 5)

- [Morphologically Symmetric Reinforcement Learning for Ambidextrous Bimanual Manipulation](https://mlsanity.com/paper/2505.05287/) (2025)
- [Beyond Topology: A Morphological Symmetry Graph Representation for Locomotion Policy Learning](https://mlsanity.com/paper/2512.00727/) (2025)
- [Morphology-Conditioned World Model for Cross-Embodiment Quadrupedal Locomotion](https://mlsanity.com/paper/2604.08780/) (2026)
- [WestWorld: A Knowledge-Encoded Scalable Trajectory World Model for Diverse Robotic Systems](https://mlsanity.com/paper/2603.14392/) (2026)
- [Morphologically Equivariant Flow Matching for Bimanual Mobile Manipulation](https://mlsanity.com/paper/2605.12228/) (2026)

## Abstract (arXiv)

We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These structural priors are embedded into the learning architecture as constraints, ensuring high generalizability, sample and model efficiency. The proposed MS-HGNN is a versatile and general architecture that is applicable to various multi-body dynamic systems and a wide range of dynamics learning problems. We formally prove the morphological-symmetry-equivariant property of our MS-HGNN and validate its effectiveness across multiple quadruped robot learning problems using both real-world and simulated data. Our code is made publicly available at https://github.com/lunarlab-gatech/MorphSym-HGNN/.