# Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification

arXiv: https://arxiv.org/abs/2506.17994 · HTML: https://mlsanity.com/paper/2506.17994/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 22 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [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)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)
- [Encoding Physical Constraints in Differentiable Newton-Euler Algorithm](https://mlsanity.com/paper/2001.08861/) (2020)
- [Structured Mechanical Models for Robot Learning and Control](https://mlsanity.com/paper/2004.10301/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes](https://mlsanity.com/paper/2004.11238/) (2020)
- [Generalized Lagrangian Neural Networks](https://mlsanity.com/paper/2401.03728/) (2024)
- [Identification of Fully Physical Consistent Inertial Parameters using Optimization on Manifolds](https://mlsanity.com/paper/1610.08703/) (2016)
- [Structured learning of rigid-body dynamics: A survey and unified view from a robotics perspective](https://mlsanity.com/paper/2012.06250/) (2020)
- [A Differentiable Newton Euler Algorithm for Multi-body Model Learning](https://mlsanity.com/paper/2010.09802/) (2020)

## Built on by (most cited first, 1 of 1)

- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)

## Abstract (arXiv)

Accurate inverse dynamics models are essential tools for controlling industrial robots. Recent research combines neural network regression with inverse dynamics formulations of the Newton-Euler and the Euler-Lagrange equations of motion, resulting in so-called Newtonian neural networks and Lagrangian neural networks, respectively. These physics-informed models seek to identify unknowns in the analytical equations from data. Despite their potential, current literature lacks guidance on choosing between Lagrangian and Newtonian networks. In this study, we show that when motor torques are estimated instead of directly measuring joint torques, Lagrangian networks prove less effective compared to Newtonian networks as they do not explicitly model dissipative torques. The performance of these models is compared to neural network regression on data of a MABI MAX 100 industrial robot.