# Denoising Hamiltonian Network for Physical Reasoning

arXiv: https://arxiv.org/abs/2503.07596 · HTML: https://mlsanity.com/paper/2503.07596/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 46 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 30 of 35)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Revisiting Self-Supervised Visual Representation Learning](https://mlsanity.com/paper/1901.09005/) (2019)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [LVSM: A Large View Synthesis Model with Minimal 3D Inductive Bias](https://mlsanity.com/paper/2410.17242/) (2024)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)

## Built on by (most cited first, 10 of 10)

- [NewtonGen: Physics-Consistent and Controllable Text-to-Video Generation via Neural Newtonian Dynamics](https://mlsanity.com/paper/2509.21309/) (2025)
- [SuperFlow: Training Flow Matching Models with RL on the Fly](https://mlsanity.com/paper/2512.17951/) (2025)
- [SeeU: Seeing the Unseen World via 4D Dynamics-aware Generation](https://mlsanity.com/paper/2512.03350/) (2025)
- [UniFlowRestore: A General Video Restoration Framework via Flow Matching and Prompt Guidance](https://mlsanity.com/paper/2504.09069/) (2025)
- [Floating-Body Hydrodynamic Neural Networks](https://mlsanity.com/paper/2509.13783/) (2025)
- [NEXUS: Neural Energy Fields for Physically Consistent Contact-Rich 3D Object Dynamics](https://mlsanity.com/paper/2606.15015/) (2026)
- [Physical Transformer](https://mlsanity.com/paper/2601.02433/) (2026)
- [CHLU: The Causal Hamiltonian Learning Unit as a Symplectic Primitive for Deep Learning](https://mlsanity.com/paper/2603.01768/) (2026)
- [Tora3: Trajectory-Guided Audio-Video Generation with Physical Coherence](https://mlsanity.com/paper/2604.09057/) (2026)
- [HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps](https://mlsanity.com/paper/2609.32838/) (2026)

## Abstract (arXiv)

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks. While these methods offer theoretical guarantees, they face two key limitations: (i) they primarily model local relations between adjacent time steps, overlooking longer-range or higher-level physical interactions, and (ii) they focus on forward simulation while neglecting broader physical reasoning tasks. We propose the Denoising Hamiltonian Network (DHN), a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. DHN also supports multi-system modeling with a global conditioning mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.