# Discovering interpretable Lagrangian of dynamical systems from data

arXiv: https://arxiv.org/abs/2302.04400 · HTML: https://mlsanity.com/paper/2302.04400/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 40 references that are in the map.
- First posted on arXiv 9 Feb 2023.

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

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [Transfer learning based multi-fidelity physics informed deep neural network](https://mlsanity.com/paper/2005.10614/) (2020)
- [Data-Driven Deep Learning of Partial Differential Equations in Modal Space](https://mlsanity.com/paper/1910.06948/) (2019)
- [Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data](https://mlsanity.com/paper/2012.02334/) (2020)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression](https://mlsanity.com/paper/2012.01937/) (2020)
- [Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Network](https://mlsanity.com/paper/2209.11588/) (2022)
- [A General Framework for Structured Learning of Mechanical Systems](https://mlsanity.com/paper/1902.08705/) (2019)
- [Model-agnostic stochastic model predictive control](https://mlsanity.com/paper/2211.13012/) (2022)

## Built on by (most cited first, 3 of 3)

- [On the definition and importance of interpretability in scientific machine learning](https://mlsanity.com/paper/2505.13510/) (2025)
- [A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2310.06241/) (2023)
- [From Data to Laws: Neural Discovery of Conservation Laws Without False Positives](https://mlsanity.com/paper/2603.20474/) (2026)

## Abstract (arXiv)

A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing equations of motion. The generalization of equation discovery techniques has huge potential; however, existing Lagrangian discovery frameworks are black-box in nature. This raises a concern about the reusability of the discovered Lagrangian. In this article, we propose a novel data-driven machine-learning algorithm to automate the discovery of interpretable Lagrangian from data. The Lagrangian are derived in interpretable forms, which also allows the automated discovery of conservation laws and governing equations of motion. The architecture of the proposed framework is designed in such a way that it allows learning the Lagrangian from a subset of the underlying domain and then generalizing for an infinite-dimensional system. The fidelity of the proposed framework is exemplified using examples described by systems of ordinary differential equations and partial differential equations where the Lagrangian and conserved quantities are known.