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Symplectic Recurrent Neural Networks

arXiv 1909.13334 ↗First posted 29 Sep 2019cs.LG stat.MLcited by 148

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Abstract (arXiv)

We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and furthermore leverages symplectic integration, multiple-step training and initial state optimization to address the challenging numerical issues associated with Hamiltonian systems. We show that SRNNs succeed reliably on complex and noisy Hamiltonian systems. We also show how to augment the SRNN integration scheme in order to handle stiff dynamical systems such as bouncing billiards.

Key facts. Cited by 148 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Sep 2019.

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Citing papers per year: 2021: 30; 2022: 36; 2023: 29; 2024: 18; 2025: 22; 2026: 13.

148 papers.

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  1. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
  2. 2022U-NO: U-shaped Neural Operatorscited by 219
  3. 2021gradSim: Differentiable simulation for system identification and visuomotor controlcited by 100
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  5. 2021UnICORNN: A recurrent model for learning very long time dependenciescited by 56
  6. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  7. 2022Generalizing to New Physical Systems via Context-Informed Dynamics Modelcited by 49
  8. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 46
  9. 2023Parallelizing non-linear sequential models over the sequence lengthcited by 45
  10. 2021Noisy Recurrent Neural Networkscited by 42
  11. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  12. 2021Long Expressive Memory for Sequence Modelingcited by 41
38 more
  1. 2021Efficient Differentiable Simulation of Articulated Bodiescited by 38
  2. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
  3. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  4. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 34
  5. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  6. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  7. 2022Thermodynamics-informed graph neural networkscited by 31
  8. 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
  9. 2022Learning continuous models for continuous physicscited by 28
  10. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  11. 2021Constraint-based graph network simulatorcited by 27
  12. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  13. 2021An Extensible Benchmark Suite for Learning to Simulate Physical Systemscited by 24
  14. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  15. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  16. 2021Adaptable Hamiltonian neural networkscited by 21
  17. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  18. 2023Learning in latent spaces improves the predictive accuracy of deep neural operatorscited by 19
  19. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 18
  20. 2021MC-LSTM: Mass-Conserving LSTMcited by 17
  21. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  22. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
  23. 2024Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systemscited by 15
  24. 2022Learning Hamiltonians of constrained mechanical systemscited by 14
  25. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  26. 2021Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memorycited by 11
  27. 2022Thermodynamics of learning physical phenomenacited by 10
  28. 2022Constants of motion networkcited by 10
  29. 2022Dynamical systems' based neural networkscited by 10
  30. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  31. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  32. 2021Structure-preserving Gaussian Process Dynamicscited by 9
  33. 2021Locally-symplectic neural networks for learning volume-preserving dynamicscited by 9
  34. 2021Learning Large-Time-Step Molecular Dynamics with Graph Neural Networkscited by 9
  35. 2022On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solvercited by 9
  36. 2022Thermodynamics-informed neural networks for physically realistic mixed realitycited by 9
  37. 2023Understanding Self-attention Mechanism via Dynamical System Perspectivecited by 9
  38. 2023Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetriescited by 9

50 most cited of 148 All 148 (JSON)