mlsanityData to 14 Oct 2026

Symplectic Neural Networks Based on Dynamical Systems

arXiv 2408.09821 ↗First posted 19 Aug 2024cs.LG cs.CE cs.NAcited by 4

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Abstract (arXiv)

We present and analyze a framework for designing symplectic neural networks (SympNets) based on geometric integrators for Hamiltonian differential equations. The SympNets are universal approximators in the space of Hamiltonian diffeomorphisms, interpretable and have a non-vanishing gradient property. We also give a representation theory for linear systems, meaning the proposed P-SympNets can exactly parameterize any symplectic map corresponding to quadratic Hamiltonians. Extensive numerical tests demonstrate increased expressiveness and accuracy -- often several orders of magnitude better -- for lower training cost over existing architectures. Lastly, we show how to perform symbolic Hamiltonian regression with SympNets for polynomial systems using backward error analysis.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 23 of its 53 references that are in the map. First posted on arXiv 19 Aug 2024.

Builds on

23 of 53 references.

References · 23

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2017Stable Architectures for Deep Neural Networkscited by 341
  3. 2019Symplectic Recurrent Neural Networkscited by 150
  4. 2019Hamiltonian Generative Networkscited by 137
  5. 2019AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networkscited by 112
  6. 2016Why does deep and cheap learning work so well?cited by 100
  7. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  8. 2019Equivariant Hamiltonian Flowscited by 39
  9. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 38
  10. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  11. 2020Nonseparable Symplectic Neural Networkscited by 31
  12. 2020Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systemscited by 24
11 more
  1. 2021Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Designcited by 18
  2. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 18
  3. 2022Learning Hamiltonians of constrained mechanical systemscited by 14
  4. 2022Learning reversible symplectic dynamicscited by 11
  5. 2022Dynamical systems' based neural networkscited by 10
  6. 2023Designing Stable Neural Networks using Convex Analysis and ODEscited by 10
  7. 2021Locally-symplectic neural networks for learning volume-preserving dynamicscited by 9
  8. 2022SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problemscited by 9
  9. 2023Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integratorscited by 4
  10. 2024Symplectic Methods in Deep Learningcited by 3
  11. 2023Universal Approximation Property of Hamiltonian Deep Neural Networkscited by 2

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Cited by year (2026 to 14 Oct)

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

4 papers.

  1. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 7
  2. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  3. 2025Neural non-canonical Hamiltonian dynamics for long-time simulationscited by 2
  4. 2026CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Liftscited by 0