# A General Framework for Structured Learning of Mechanical Systems

arXiv: https://arxiv.org/abs/1902.08705 · HTML: https://mlsanity.com/paper/1902.08705/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2019.

## Built on by (most cited first, 13 of 13)

- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Generalized Lagrangian Neural Networks](https://mlsanity.com/paper/2401.03728/) (2024)
- [Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution](https://mlsanity.com/paper/2308.14666/) (2023)
- [Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body](https://mlsanity.com/paper/2209.11355/) (2022)
- [Learning Modular Simulations for Homogeneous Systems](https://mlsanity.com/paper/2210.16294/) (2022)
- [Discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2302.04400/) (2023)
- [Training Structured Mechanical Models by Minimizing Discrete Euler-Lagrange Residual](https://mlsanity.com/paper/2105.01811/) (2021)
- [Lagrangian Density Space-Time Deep Neural Network Topology](https://mlsanity.com/paper/2207.12209/) (2022)
- [Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Framework](https://mlsanity.com/paper/2403.08194/) (2024)

## Abstract (arXiv)

Learning accurate dynamics models is necessary for optimal, compliant control of robotic systems. Current approaches to white-box modeling using analytic parameterizations, or black-box modeling using neural networks, can suffer from high bias or high variance. We address the need for a flexible, gray-box model of mechanical systems that can seamlessly incorporate prior knowledge where it is available, and train expressive function approximators where it is not. We propose to parameterize a mechanical system using neural networks to model its Lagrangian and the generalized forces that act on it. We test our method on a simulated, actuated double pendulum. We show that our method outperforms a naive, black-box model in terms of data-efficiency, as well as performance in model-based reinforcement learning. We also conduct a systematic study of our method's ability to incorporate available prior knowledge about the system to improve data efficiency.