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

Max Tegmark (MIT); Ziming Liu (MIT)

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2011.04698 v2 pith:VRSMTVZK submitted 2020-11-09 cs.LG astro-ph.EPnlin.SIphysics.class-ph

Ziming Liu (MIT) , Max Tegmark (MIT) This is my paper · ORCID

classification cs.LGastro-ph.EPnlin.SIphysics.class-ph

keywords conservationconservedlawslearningmachinepoincarquantitiessystems

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original abstract

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Machine-Learning Search for Lax Connections
hep-th 2026-08 conditional novelty 5.0 of 10

An ML search for Lax connections recovers known spectral-parameter families in SU(2) PCM and S^2, but the low-loss candidate found for the non-symmetric coset T^{1,1} is a fake Lax connection, not a genuine integrabil...

Pith tools