mlsanityData to 14 Oct 2026

Discovering New Interpretable Conservation Laws as Sparse Invariants

arXiv 2305.19525 ↗First posted 31 May 2023math.DS cs.LG nlin.SIcited by 1

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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.

Key facts. Cited by 1 paper 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

6 of 16 references.

References · 6

  1. 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
  2. 2020Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networkscited by 33
  3. 2022AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equationscited by 20
  4. 2018Discovering conservation laws from data for controlcited by 14
  5. 2019Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networkscited by 10
  6. 2022Constants of motion networkcited by 10

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Citing papers per year: 2025: 1.

1 paper.

  1. 2025Interpretable Machine Learning in Physics: A Reviewcited by 14