# Model-agnostic machine learning of conservation laws from data

arXiv: https://arxiv.org/abs/2301.07503 · HTML: https://mlsanity.com/paper/2301.07503/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 12 Jan 2023.

## Builds on (most cited first, 4 of 4)

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equations](https://mlsanity.com/paper/2203.12610/) (2022)
- [Discovering conservation laws from trajectories via machine learning](https://mlsanity.com/paper/2102.04008/) (2021)

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

- [Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation](https://mlsanity.com/paper/2410.05445/) (2024)

## Abstract (arXiv)

We present a machine learning based method for learning first integrals of systems of ordinary differential equations from given trajectory data. The method is model-agnostic in that it does not require explicit knowledge of the underlying system of differential equations that generated the trajectories. As a by-product, once the first integrals have been learned, also the system of differential equations will be known. We illustrate our method by considering several classical problems from the mathematical sciences.