mlsanityData to 7 Oct 2026

Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately

arXiv 2201.10085 ↗First posted 25 Jan 2022cs.LG cs.NEcited by 46

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Abstract (arXiv)

Understanding natural symmetries is key to making sense of our complex and ever-changing world. Recent work has shown that neural networks can learn such symmetries directly from data using Hamiltonian Neural Networks (HNNs). But HNNs struggle when trained on datasets where energy is not conserved. In this paper, we ask whether it is possible to identify and decompose conservative and dissipative dynamics simultaneously. We propose Dissipative Hamiltonian Neural Networks (D-HNNs), which parameterize both a Hamiltonian and a Rayleigh dissipation function. Taken together, they represent an implicit Helmholtz decomposition which can separate dissipative effects such as friction from symmetries such as conservation of energy. We train our model to decompose a damped mass-spring system into its friction and inertial terms and then show that this decomposition can be used to predict dynamics for unseen friction coefficients. Then we apply our model to real world data including a large, noisy ocean current dataset where decomposing the velocity field yields useful scientific insights.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Builds on 11 of its 32 references that are in the map. First posted on arXiv 25 Jan 2022.

Builds on

11 of 32 references.

References · 11

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
  4. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  5. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
  6. 2019Symplectic Recurrent Neural Networkscited by 148
  7. 2019Hamiltonian Generative Networkscited by 136
  8. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  9. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
  10. 2020TensorFlow Quantum: A Software Framework for Quantum Machine Learningcited by 72
  11. 2019Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Videocited by 43

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 5; 2024: 9; 2025: 9; 2026: 17.

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  1. 2022Neural Implicit Representations for Physical Parameter Inference from a Single Videocited by 19
  2. 2023Gaussian processes at the Helm(holtz): A more fluid model for ocean currentscited by 11
  3. 2022Constants of motion networkcited by 10
  4. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  5. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  6. 2023Symmetry Preservation in Hamiltonian Systems: Simulation and Learningcited by 6
  7. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 6
  8. 2024Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structurecited by 6
  9. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 6
  10. 2022Unifying physical systems' inductive biases in neural ODE using dynamics constraintscited by 5
  11. 2023Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Modelscited by 5
  12. 2025MetaSym: A Symplectic Meta-learning Framework for Physical Intelligencecited by 5
34 more
  1. 2025SlotPi: Physics-informed Object-centric Reasoning Modelscited by 5
  2. 2024A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networkscited by 4
  3. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  4. 2025Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systemscited by 3
  5. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  6. 2024Lagrangian Neural Networks for Reversible Dissipative Evolutioncited by 2
  7. 2024Physics-informed Imitative Reinforcement Learning for Real-world Drivingcited by 2
  8. 2024Training Hamiltonian neural networks without backpropagationcited by 2
  9. 2025Geometric Contact Flows: Contactomorphisms for Dynamics and Controlcited by 2
  10. 2025Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approachcited by 2
  11. 2026PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecastingcited by 2
  12. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1
  13. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  14. 2026Physics-informed Diffusion Mamba Transformer for Real-world Drivingcited by 1
  15. 2026Controlled oscillation modeling using port-Hamiltonian neural networkscited by 1
  16. 2026Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networkscited by 1
  17. 2026Metriplector: From Field Theory to Neural Architecturecited by 1
  18. 2026Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Datacited by 1
  19. 2026NEXUS: Neural Energy Fields for Physically Consistent Contact-Rich 3D Object Dynamicscited by 1
  20. 2026CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systemscited by 1
  21. 2026History-informed Lagrangian Neural Networkscited by 1
  22. 2022KeyCLD: Learning Constrained Lagrangian Dynamics in Keypoint Coordinates from Imagescited by 0
  23. 2024Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEscited by 0
  24. 2024Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier featurescited by 0
  25. 2024Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?cited by 0
  26. 2025Mass Conservation on Rails -- Rethinking Physics-Informed Learning of Ice Flow Vector Fieldscited by 0
  27. 2026Momentum-Conserving Graph Neural Networks for Deformable Objectscited by 0
  28. 2026Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equationscited by 0
  29. 2026CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Liftscited by 0
  30. 2026CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamicscited by 0
  31. 2026Learning Deterministic and Stochastic Forced Hamiltonian Systemscited by 0
  32. 2026Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Modelscited by 0
  33. 2026HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Mapscited by 0
  34. 2026Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physicscited by 0