mlsanityData to 7 Oct 2026

AI Poincar'e 2.0: Machine Learning Conservation Laws from Differential Equations

arXiv 2203.12610 ↗First posted 23 Mar 2022cs.LG astro-ph.EP nlin.SIcited by 20

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Abstract (arXiv)

We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schr"odinger equation.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 10 of its 27 references that are in the map. First posted on arXiv 23 Mar 2022.

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10 of 27 references.

References · 10

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  3. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  4. 2020AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularitycited by 140
  5. 2020Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamicscited by 93
  6. 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
  7. 2020Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networkscited by 33
  8. 2021Machine-learning hidden symmetriescited by 31
  9. 2019Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learningcited by 15
  10. 2019Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networkscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 5; 2024: 3; 2025: 5; 2026: 4.

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  1. 2022Discovering Conservation Laws using Optimal Transport and Manifold Learningcited by 12
  2. 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
  3. 2022Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regressioncited by 8
  4. 2026From Kepler to Newton: Inductive Biases Guide Learned World Models in Transformerscited by 6
  5. 2023ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Predictioncited by 5
  6. 2025AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledgecited by 5
  7. 2024Exploring the Truth and Beauty of Theory Landscapes with Machine Learningcited by 4
  8. 2024Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflationcited by 3
  9. 2023Seeking Truth and Beauty in Flavor Physics with Machine Learningcited by 2
  10. 2025Learning finite symmetry groups of dynamical systems via equivariance detectioncited by 2
  11. 2023Model-agnostic machine learning of conservation laws from datacited by 1
  12. 2023Discovering New Interpretable Conservation Laws as Sparse Invariantscited by 1
8 more
  1. 2024Discover physical concepts and equations with machine learningcited by 1
  2. 2025Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approachcited by 1
  3. 2025Discovering Symmetries of ODEs by Symbolic Regressioncited by 1
  4. 2026Symmetry-Constrained Language-Guided Program Synthesis for Discovering Governing Equations from Noisy and Partial Observationscited by 1
  5. 2022Learning quantum symmetries with interactive quantum-classical variational algorithmscited by 0
  6. 2023A charge-preserving method for solving graph neural diffusion networkscited by 0
  7. 2026From Data to Laws: Neural Discovery of Conservation Laws Without False Positivescited by 0
  8. 2026Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learningcited by 0