# Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately

arXiv: https://arxiv.org/abs/2201.10085 · HTML: https://mlsanity.com/paper/2201.10085/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 25 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Video](https://mlsanity.com/paper/1905.11169/) (2019)

## Built on by (most cited first, 30 of 47)

- [Neural Implicit Representations for Physical Parameter Inference from a Single Video](https://mlsanity.com/paper/2204.14030/) (2022)
- [Gaussian processes at the Helm(holtz): A more fluid model for ocean currents](https://mlsanity.com/paper/2302.10364/) (2023)
- [Constants of motion network](https://mlsanity.com/paper/2208.10387/) (2022)
- [Pseudo-Hamiltonian neural networks for learning partial differential equations](https://mlsanity.com/paper/2304.14374/) (2023)
- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics](https://mlsanity.com/paper/2505.20370/) (2025)
- [Symmetry Preservation in Hamiltonian Systems: Simulation and Learning](https://mlsanity.com/paper/2308.16331/) (2023)
- [Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure](https://mlsanity.com/paper/2401.04986/) (2024)
- [Unifying physical systems' inductive biases in neural ODE using dynamics constraints](https://mlsanity.com/paper/2208.02632/) (2022)
- [Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Models](https://mlsanity.com/paper/2305.01338/) (2023)
- [MetaSym: A Symplectic Meta-learning Framework for Physical Intelligence](https://mlsanity.com/paper/2502.16667/) (2025)
- [SlotPi: Physics-informed Object-centric Reasoning Models](https://mlsanity.com/paper/2506.10778/) (2025)
- [A comparison of Single- and Double-generator formalisms for Thermodynamics-Informed Neural Networks](https://mlsanity.com/paper/2404.01060/) (2024)
- [Symplectic Neural Flows for Modeling and Discovery](https://mlsanity.com/paper/2412.16787/) (2024)
- [Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systems](https://mlsanity.com/paper/2501.07373/) (2025)
- [Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems](https://mlsanity.com/paper/2508.12569/) (2025)
- [Lagrangian Neural Networks for Reversible Dissipative Evolution](https://mlsanity.com/paper/2405.14645/) (2024)
- [Physics-informed Imitative Reinforcement Learning for Real-world Driving](https://mlsanity.com/paper/2407.02508/) (2024)
- [Training Hamiltonian neural networks without backpropagation](https://mlsanity.com/paper/2411.17511/) (2024)
- [Geometric Contact Flows: Contactomorphisms for Dynamics and Control](https://mlsanity.com/paper/2506.17868/) (2025)
- [Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach](https://mlsanity.com/paper/2509.24627/) (2025)
- [PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting](https://mlsanity.com/paper/2602.17998/) (2026)
- [Metriplector: From Field Theory to Neural Architecture](https://mlsanity.com/paper/2603.29496/) (2026)
- [Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian](https://mlsanity.com/paper/2210.00090/) (2022)
- [Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data](https://mlsanity.com/paper/2509.07280/) (2025)
- [Physics-informed Diffusion Mamba Transformer for Real-world Driving](https://mlsanity.com/paper/2602.00808/) (2026)
- [Controlled oscillation modeling using port-Hamiltonian neural networks](https://mlsanity.com/paper/2602.15704/) (2026)
- [Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networks](https://mlsanity.com/paper/2603.27442/) (2026)
- [Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data](https://mlsanity.com/paper/2604.17470/) (2026)

## 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.