# Learning Forced Multibody Dynamics on Lie Groups

arXiv: https://arxiv.org/abs/2607.12627 · HTML: https://mlsanity.com/paper/2607.12627/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Direct Sparse Odometry](https://mlsanity.com/paper/1607.02565/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Structure preserving deep learning](https://mlsanity.com/paper/2006.03364/) (2020)
- [Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems](https://mlsanity.com/paper/2005.04986/) (2020)
- [The invariant extended Kalman filter as a stable observer](https://mlsanity.com/paper/1410.1465/) (2014)
- [Generalized Lagrangian Neural Networks](https://mlsanity.com/paper/2401.03728/) (2024)
- [Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems](https://mlsanity.com/paper/2211.16006/) (2022)
- [Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics](https://mlsanity.com/paper/2505.20370/) (2025)

## Abstract (arXiv)

We propose an architecture for learning the dynamics of mechanical systems based on discrete forced Euler-Lagrange equations on Lie groups using only position data. By formulating the dynamics directly on manifold-valued configuration spaces, the method naturally respects the geometric structure of the systems and preserves geometric invariants and conservation laws. The reliance on position measurements alone makes the framework applicable in settings where velocity data are unavailable or noisy. The approach extends naturally to multibody systems, accommodates external control inputs, and demonstrates strong performance on both synthetic and real-world datasets.