# Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements

arXiv: https://arxiv.org/abs/2512.03035 · HTML: https://mlsanity.com/paper/2512.03035/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling](https://mlsanity.com/paper/2109.05364/) (2021)
- [Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2212.00893/) (2022)
- [Multiple shooting for training neural differential equations on time series](https://mlsanity.com/paper/2109.06786/) (2021)
- [How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.06335/) (2023)
- [Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Models](https://mlsanity.com/paper/2305.01338/) (2023)
- [Floating-Base Deep Lagrangian Networks](https://mlsanity.com/paper/2510.17270/) (2025)

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

- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)

## Abstract (arXiv)

This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification of physically consistent models, which are essential for model-based control synthesis. Lagrangian or Hamiltonian neural networks provide useful structural guarantees but the learning of such models often leads to inconsistent models, especially on real physical systems where training data are limited, partial and noisy. Motivated by this observation and the objective to exploit these models for model-based nonlinear control, a learning algorithm relying on an original loss function is proposed to improve the physical consistency of Lagrangian systems. A comparative analysis of different learning-based modeling approaches with the proposed solution shows significant improvements in terms of physical consistency of the learned models, on both simulated and experimental systems. The model's consistency is then exploited to demonstrate, on an experimental benchmark, the practical relevance of the proposed methodology for feedback linearization and energy-based control techniques.