# Hamiltonian Neural Networks

arXiv: https://arxiv.org/abs/1906.01563 · HTML: https://mlsanity.com/paper/1906.01563/

## Key facts

- Cited by 712 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2019.

## Built on by (most cited first, 30 of 712)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Lie Point Symmetry Data Augmentation for Neural PDE Solvers](https://mlsanity.com/paper/2202.07643/) (2022)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Robot Learning from Randomized Simulations: A Review](https://mlsanity.com/paper/2111.00956/) (2021)
- [A Dynamical System Perspective for Lipschitz Neural Networks](https://mlsanity.com/paper/2110.12690/) (2021)
- [Scientific Machine Learning Benchmarks](https://mlsanity.com/paper/2110.12773/) (2021)
- [Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling](https://mlsanity.com/paper/2102.13156/) (2021)
- [UnICORNN: A recurrent model for learning very long time dependencies](https://mlsanity.com/paper/2103.05487/) (2021)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints](https://mlsanity.com/paper/2506.04171/) (2025)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Parallelizing non-linear sequential models over the sequence length](https://mlsanity.com/paper/2309.12252/) (2023)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Noisy Recurrent Neural Networks](https://mlsanity.com/paper/2102.04877/) (2021)

## Abstract (arXiv)

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.