# Dissipative Lagrangian Neural Networks for the Interpretable Modelling of Passive Mechanical Systems

arXiv: https://arxiv.org/abs/2610.15996 · HTML: https://mlsanity.com/paper/2610.15996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 11 Oct 2026.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [How to Train Your Robot with Deep Reinforcement Learning; Lessons We've Learned](https://mlsanity.com/paper/2102.02915/) (2021)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [A spectrum of physics-informed Gaussian processes for regression in engineering](https://mlsanity.com/paper/2309.10656/) (2023)
- [Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations](https://mlsanity.com/paper/2405.05987/) (2024)
- [Generalized Lagrangian Neural Networks](https://mlsanity.com/paper/2401.03728/) (2024)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics](https://mlsanity.com/paper/2505.20370/) (2025)
- [Learning Relativistic Geodesics and Chaotic Dynamics via Stabilized Lagrangian Neural Networks](https://mlsanity.com/paper/2601.12519/) (2026)

## Abstract (arXiv)

In this paper, we propose the Dissipative Lagrangian Neural Network (dLNN), a continuous-time system identification technique that separately learns the conservative and dissipative dynamics of a mechanical system directly from data. A key contribution is a novel parametrisation of dissipative forces that (i) is structurally constrained to be dissipative, enforcing passivity of the learned model, (ii) cannot absorb conservative mechanics, and (iii) retains sufficient expressivity to represent a broad family of state-dependent damping and regularised friction forces. The model is validated on prediction tasks on two real-world mechanical systems: trajectory prediction of a chaotic double pendulum and inverse-dynamics modelling of a six-degree-of-freedom industrial robot. Across these tasks, the dLNN demonstrates improved predictive performance over existing Lagrangian architectures while remaining competitive with a black-box neural model. The imposed physical structure also improves generalisation to unseen states, with the benefits becoming particularly pronounced when training data is limited. Finally, we introduce a symbolic distillation procedure that extracts closed-form expressions from the learned physical components. Applied to the industrial robot, this produces interpretable symbolic models that retain high predictive accuracy while reducing the computational overhead associated with evaluating neural Lagrangian models.