# Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Network

arXiv: https://arxiv.org/abs/2209.11588 · HTML: https://mlsanity.com/paper/2209.11588/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 17 of 17)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data](https://mlsanity.com/paper/2012.02334/) (2020)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics](https://mlsanity.com/paper/2005.14617/) (2020)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Constraint-based graph network simulator](https://mlsanity.com/paper/2112.09161/) (2021)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
- [Learning Physical Constraints with Neural Projections](https://mlsanity.com/paper/2006.12745/) (2020)
- [Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networks](https://mlsanity.com/paper/2209.01476/) (2022)

## Built on by (most cited first, 23 of 23)

- [Global Counterfactual Explainer for Graph Neural Networks](https://mlsanity.com/paper/2210.11695/) (2022)
- [Mirage: Model-Agnostic Graph Distillation for Graph Classification](https://mlsanity.com/paper/2310.09486/) (2023)
- [GNNX-BENCH: Unravelling the Utility of Perturbation-based GNN Explainers through In-depth Benchmarking](https://mlsanity.com/paper/2310.01794/) (2023)
- [GRAFENNE: Learning on Graphs with Heterogeneous and Dynamic Feature Sets](https://mlsanity.com/paper/2306.03447/) (2023)
- [StriderNET: A Graph Reinforcement Learning Approach to Optimize Atomic Structures on Rough Energy Landscapes](https://mlsanity.com/paper/2301.12477/) (2023)
- [Discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2302.04400/) (2023)
- [Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systems](https://mlsanity.com/paper/2501.07373/) (2025)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics](https://mlsanity.com/paper/2306.11435/) (2023)
- [Discovering Symbolic Laws Directly from Trajectories with Hamiltonian Graph Neural Networks](https://mlsanity.com/paper/2307.05299/) (2023)
- [A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2310.06241/) (2023)
- [Rapid training of Hamiltonian graph networks using random features](https://mlsanity.com/paper/2506.06558/) (2025)
- [Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Framework](https://mlsanity.com/paper/2512.15767/) (2025)
- [Super-resolution of turbulent reacting flows on complex meshes using graph neural networks](https://mlsanity.com/paper/2603.01080/) (2026)
- [Bonsai: Gradient-free Graph Condensation for Node Classification](https://mlsanity.com/paper/2410.17579/) (2024)
- [Do Two AI Scientists Agree?](https://mlsanity.com/paper/2504.02822/) (2025)
- [COMRECGC: Global Graph Counterfactual Explainer through Common Recourse](https://mlsanity.com/paper/2505.07081/) (2025)
- [TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows](https://mlsanity.com/paper/2508.05070/) (2025)
- [Rigid Body Adversarial Attacks](https://mlsanity.com/paper/2502.05669/) (2025)
- [HYPERPOSE: Hyperbolic Kinematic Phase-Space Attention for 3D Human Pose Estimation](https://mlsanity.com/paper/2605.10100/) (2026)
- [GFFMERGE: Efficient Merging of Graph Neural Force Fields and Beyond](https://mlsanity.com/paper/2606.03232/) (2026)
- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)
- [Recovering Irreducible Three-Body Interactions with Lagrangian Neural Networks](https://mlsanity.com/paper/2610.13292/) (2026)

## Abstract (arXiv)

Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited to simple systems such as pendulums and springs or a single rigid body such as a gyroscope or a rigid rotor. Here, we present a Lagrangian graph neural network (LGNN) that can learn the dynamics of articulated rigid bodies by exploiting their topology. We demonstrate the performance of LGNN by learning the dynamics of ropes, chains, and trusses with the bars modeled as rigid bodies. LGNN also exhibits generalizability -- LGNN trained on chains with a few segments exhibits generalizability to simulate a chain with large number of links and arbitrary link length. We also show that the LGNN can simulate unseen hybrid systems including bars and chains, on which they have not been trained on. Specifically, we show that the LGNN can be used to model the dynamics of complex real-world structures such as the stability of tensegrity structures. Finally, we discuss the non-diagonal nature of the mass matrix and its ability to generalize in complex systems.