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Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning

arXiv 2002.08860 ↗First posted 20 Feb 2020cs.LG cs.SY eess.SYcited by 77

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Abstract (arXiv)

In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and potential energy, paves the way for energy-based controllers.

Key facts. Cited by 77 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 15; 2022: 18; 2023: 13; 2024: 8; 2025: 11; 2026: 12.

77 papers.

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  1. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
  2. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  3. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 46
  4. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  5. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
  6. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  7. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  8. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  9. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  10. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  11. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  12. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
38 more
  1. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  2. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  3. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  4. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 17
  5. 2022Physics-Informed Model-Based Reinforcement Learningcited by 17
  6. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  7. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  8. 2022Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networkscited by 11
  9. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  10. 2021Machine-Learning Non-Conservative Dynamics for New-Physics Detectioncited by 10
  11. 2022Thermodynamics of learning physical phenomenacited by 10
  12. 2022Constants of motion networkcited by 10
  13. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  14. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  15. 2025Denoising Hamiltonian Network for Physical Reasoningcited by 10
  16. 2024Physics-Informed Regularization for Domain-Agnostic Dynamical System Modelingcited by 9
  17. 2021Identifying Physical Law of Hamiltonian Systems via Meta-Learningcited by 8
  18. 2021Weak Form Generalized Hamiltonian Learningcited by 8
  19. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  20. 2022Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systemscited by 7
  21. 2023Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distributioncited by 7
  22. 2022Approximation of nearly-periodic symplectic maps via structure-preserving neural networkscited by 6
  23. 2023Uncertainty and Structure in Neural Ordinary Differential Equationscited by 6
  24. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 6
  25. 2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
  26. 2022Unifying physical systems' inductive biases in neural ODE using dynamics constraintscited by 5
  27. 2023Learning Dissipative Neural Dynamical Systemscited by 5
  28. 2025MetaSym: A Symplectic Meta-learning Framework for Physical Intelligencecited by 5
  29. 2021Optimal Energy Shaping via Neural Approximatorscited by 4
  30. 2022Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Bodycited by 4
  31. 2023Hamiltonian GANcited by 4
  32. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  33. 2023Discovering interpretable Lagrangian of dynamical systems from datacited by 3
  34. 2023Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamicscited by 3
  35. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  36. 2024Training Hamiltonian neural networks without backpropagationcited by 2
  37. 2025Geometric Contact Flows: Contactomorphisms for Dynamics and Controlcited by 2
  38. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2

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