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AI Poincar'e: Machine Learning Conservation Laws from Trajectories

arXiv 2011.04698 ↗First posted 9 Nov 2020cs.LG astro-ph.EP nlin.SIcited by 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.

Key facts. Cited by 77 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Nov 2020.

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Citing papers per year: 2021: 7; 2022: 10; 2023: 24; 2024: 14; 2025: 14; 2026: 8.

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50 most cited of 77 All 77 (JSON)