mlsanityData to 14 Oct 2026

Constants of motion network

arXiv 2208.10387 ↗First posted 22 Aug 2022cs.LG cs.AI physics.class-phcited by 10

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Abstract (arXiv)

The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically requires mathematical proficiency and manual analytical work. In this paper, we present a neural network that can simultaneously learn the dynamics of the system and the constants of motion from data. By exploiting the discovered constants of motion, it can produce better predictions on dynamics and can work on a wider range of systems than Hamiltonian-based neural networks. In addition, the training progresses of our method can be used as an indication of the number of constants of motion in a system which could be useful in studying a novel physical system.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 15 of its 40 references that are in the map. First posted on arXiv 22 Aug 2022.

Builds on

15 of 40 references.

References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2019Hamiltonian Neural Networkscited by 712
  4. 2020Lagrangian Neural Networkscited by 398
  5. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  6. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  7. 2019Symplectic Recurrent Neural Networkscited by 150
  8. 2019Hamiltonian Generative Networkscited by 137
  9. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  10. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 79
  11. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 47
  12. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 38
3 more
  1. 2020Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physicscited by 36
  2. 2021Learning the exchange-correlation functional from nature with fully differentiable density functional theorycited by 23
  3. 2021Adaptable Hamiltonian neural networkscited by 21

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 1; 2024: 2; 2025: 4; 2026: 1.

10 papers.

  1. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 52
  2. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  3. 2025End-to-End Probabilistic Framework for Learning with Hard Constraintscited by 9
  4. 2024Projected Neural Differential Equations for Learning Constrained Dynamicscited by 5
  5. 2025Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraintscited by 4
  6. 2022Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learningcited by 3
  7. 2025Discovering Phase Space Structure in Learned Hamiltonian Systemscited by 2
  8. 2023Discovering New Interpretable Conservation Laws as Sparse Invariantscited by 1
  9. 2024Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domainscited by 1
  10. 2026Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learningcited by 0