# Hamiltonian GAN

arXiv: https://arxiv.org/abs/2308.11216 · HTML: https://mlsanity.com/paper/2308.11216/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 37 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [MoCoGAN: Decomposing Motion and Content for Video Generation](https://mlsanity.com/paper/1707.04993/) (2017)
- [Generating Videos with Scene Dynamics](https://mlsanity.com/paper/1609.02612/) (2016)
- [StyleGAN-V: A Continuous Video Generator with the Price, Image Quality and Perks of StyleGAN2](https://mlsanity.com/paper/2112.14683/) (2021)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Generating Videos with Dynamics-aware Implicit Generative Adversarial Networks](https://mlsanity.com/paper/2202.10571/) (2022)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [A Good Image Generator Is What You Need for High-Resolution Video Synthesis](https://mlsanity.com/paper/2104.15069/) (2021)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control](https://mlsanity.com/paper/2007.01926/) (2020)
- [Variational Integrator Networks for Physically Structured Embeddings](https://mlsanity.com/paper/1910.09349/) (2019)
- [Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics](https://mlsanity.com/paper/2005.14617/) (2020)
- [Which priors matter? Benchmarking models for learning latent dynamics](https://mlsanity.com/paper/2111.05458/) (2021)
- [LagNetViP: A Lagrangian Neural Network for Video Prediction](https://mlsanity.com/paper/2010.12932/) (2020)
- [Latent Neural Differential Equations for Video Generation](https://mlsanity.com/paper/2011.03864/) (2020)
- [SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision](https://mlsanity.com/paper/2111.05986/) (2021)

## Built on by (most cited first, 4 of 4)

- [Behavior-Inspired Neural Networks for Relational Inference](https://mlsanity.com/paper/2406.14746/) (2024)
- [Discovering Phase Space Structure in Learned Hamiltonian Systems](https://mlsanity.com/paper/2509.23003/) (2025)
- [Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamics](https://mlsanity.com/paper/2603.06354/) (2026)
- [Generating Physically Plausible Parachute Dynamics with Deep Generative Modeling](https://mlsanity.com/paper/2607.12143/) (2026)

## Abstract (arXiv)

A growing body of work leverages the Hamiltonian formalism as an inductive bias for physically plausible neural network based video generation. The structure of the Hamiltonian ensures conservation of a learned quantity (e.g., energy) and imposes a phase-space interpretation on the low-dimensional manifold underlying the input video. While this interpretation has the potential to facilitate the integration of learned representations in downstream tasks, existing methods are limited in their applicability as they require a structural prior for the configuration space at design time. In this work, we present a GAN-based video generation pipeline with a learned configuration space map and Hamiltonian neural network motion model, to learn a representation of the configuration space from data. We train our model with a physics-inspired cyclic-coordinate loss function which encourages a minimal representation of the configuration space and improves interpretability. We demonstrate the efficacy and advantages of our approach on the Hamiltonian Dynamics Suite Toy Physics dataset.