# Generalized Lagrangian Neural Networks

arXiv: https://arxiv.org/abs/2401.03728 · HTML: https://mlsanity.com/paper/2401.03728/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 21 of 21)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control](https://mlsanity.com/paper/2007.01926/) (2020)
- [OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle](https://mlsanity.com/paper/2009.02327/) (2020)
- [Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems](https://mlsanity.com/paper/2005.04986/) (2020)
- [Reversible Recurrent Neural Networks](https://mlsanity.com/paper/1810.10999/) (2018)
- [Learning Symmetries of Classical Integrable Systems](https://mlsanity.com/paper/1906.04645/) (2019)
- [A General Framework for Structured Learning of Mechanical Systems](https://mlsanity.com/paper/1902.08705/) (2019)
- [Achieving Constraints in Neural Networks: A Stochastic Augmented Lagrangian Approach](https://mlsanity.com/paper/2310.16647/) (2023)

## Built on by (most cited first, 10 of 10)

- [Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics](https://mlsanity.com/paper/2505.20370/) (2025)
- [Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems](https://mlsanity.com/paper/2508.12569/) (2025)
- [Lagrangian Neural Networks for Reversible Dissipative Evolution](https://mlsanity.com/paper/2405.14645/) (2024)
- [Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification](https://mlsanity.com/paper/2506.17994/) (2025)
- [A neural operator for predicting vibration frequency response curves from limited data](https://mlsanity.com/paper/2603.10149/) (2026)
- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)
- [Learning Forced Multibody Dynamics on Lie Groups](https://mlsanity.com/paper/2607.12627/) (2026)
- [Learning Deterministic and Stochastic Forced Hamiltonian Systems](https://mlsanity.com/paper/2608.19688/) (2026)
- [LagrangeGS: Non-Conservative Lagrangian System on Dynamic 3D Gaussian Splatting](https://mlsanity.com/paper/2608.22773/) (2026)
- [Dissipative Lagrangian Neural Networks for the Interpretable Modelling of Passive Mechanical Systems](https://mlsanity.com/paper/2610.15996/) (2026)

## Abstract (arXiv)

Incorporating neural networks for the solution of Ordinary Differential Equations (ODEs) represents a pivotal research direction within computational mathematics. Within neural network architectures, the integration of the intrinsic structure of ODEs offers advantages such as enhanced predictive capabilities and reduced data utilization. Among these structural ODE forms, the Lagrangian representation stands out due to its significant physical underpinnings. Building upon this framework, Bhattoo introduced the concept of Lagrangian Neural Networks (LNNs). Then in this article, we introduce a groundbreaking extension (Genralized Lagrangian Neural Networks) to Lagrangian Neural Networks (LNNs), innovatively tailoring them for non-conservative systems. By leveraging the foundational importance of the Lagrangian within Lagrange's equations, we formulate the model based on the generalized Lagrange's equation. This modification not only enhances prediction accuracy but also guarantees Lagrangian representation in non-conservative systems. Furthermore, we perform various experiments, encompassing 1-dimensional and 2-dimensional examples, along with an examination of the impact of network parameters, which proved the superiority of Generalized Lagrangian Neural Networks(GLNNs).