# A Differentiable Newton Euler Algorithm for Multi-body Model Learning

arXiv: https://arxiv.org/abs/2010.09802 · HTML: https://mlsanity.com/paper/2010.09802/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)
- [Learning Dynamics Models for Model Predictive Agents](https://mlsanity.com/paper/2109.14311/) (2021)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [A Recurrent Differentiable Engine for Modeling Tensegrity Robots Trainable with Low-Frequency Data](https://mlsanity.com/paper/2203.00041/) (2022)
- [Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification](https://mlsanity.com/paper/2506.17994/) (2025)
- [Bayesian Inverse Physics for Neuro-Symbolic Robot Learning](https://mlsanity.com/paper/2506.08756/) (2025)

## Abstract (arXiv)

In this work, we examine a spectrum of hybrid model for the domain of multi-body robot dynamics. We motivate a computation graph architecture that embodies the Newton Euler equations, emphasizing the utility of the Lie Algebra form in translating the dynamical geometry into an efficient computational structure for learning. We describe the used virtual parameters that enable unconstrained physical plausible dynamics and the used actuator models. In the experiments, we define a family of 26 grey-box models and evaluate them for system identification of the simulated and physical Furuta Pendulum and Cartpole. The comparison shows that the kinematic parameters, required by previous white-box system identification methods, can be accurately inferred from data. Furthermore, we highlight that models with guaranteed bounded energy of the uncontrolled system generate non-divergent trajectories, while more general models have no such guarantee, so their performance strongly depends on the data distribution. Therefore, the main contributions of this work is the introduction of a white-box model that jointly learns dynamic and kinematics parameters and can be combined with black-box components. We then provide extensive empirical evaluation on challenging systems and different datasets that elucidates the comparative performance of our grey-box architecture with comparable white- and black-box models.