# Discovering New Interpretable Conservation Laws as Sparse Invariants

arXiv: https://arxiv.org/abs/2305.19525 · HTML: https://mlsanity.com/paper/2305.19525/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 6 of 6)

- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)
- [AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equations](https://mlsanity.com/paper/2203.12610/) (2022)
- [Discovering conservation laws from data for control](https://mlsanity.com/paper/1811.00961/) (2018)
- [Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networks](https://mlsanity.com/paper/2001.00111/) (2019)
- [Constants of motion network](https://mlsanity.com/paper/2208.10387/) (2022)

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

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)

## Abstract (arXiv)

Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equations and basis functions are both known), we propose the Sparse Invariant Detector (SID), an algorithm that auto-discovers conservation laws from differential equations. Its algorithmic simplicity allows robustness and interpretability of the discovered conserved quantities. We show that SID is able to rediscover known and even discover new conservation laws in a variety of systems. For two examples in fluid mechanics and atmospheric chemistry, SID discovers 14 and 3 conserved quantities, respectively, where only 12 and 2 were previously known to domain experts.