# AI Poincar'e: Machine Learning Conservation Laws from Trajectories

arXiv: https://arxiv.org/abs/2011.04698 · HTML: https://mlsanity.com/paper/2011.04698/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 30 of 77)

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## Abstract (arXiv)

We present AI Poincar'e, a machine learning algorithm for auto-discovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational 3-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions and breakdown timescales for approximate conservation laws.