# HamNet: Conformation-Guided Molecular Representation with Hamiltonian Neural Networks

arXiv: https://arxiv.org/abs/2105.03688 · HTML: https://mlsanity.com/paper/2105.03688/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 8 May 2021.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Three-Dimensionally Embedded Graph Convolutional Network (3DGCN) for Molecule Interpretation](https://mlsanity.com/paper/1811.09794/) (2018)
- [TF3P: Three-dimensional Force Fields Fingerprint Learned by Deep Capsular Network](https://mlsanity.com/paper/1912.11430/) (2019)

## Built on by (most cited first, 13 of 13)

- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [The Exact Sample Complexity Gain from Invariances for Kernel Regression](https://mlsanity.com/paper/2303.14269/) (2023)
- [Deep Molecular Representation Learning via Fusing Physical and Chemical Information](https://mlsanity.com/paper/2112.04624/) (2021)
- [DenseGNN: universal and scalable deeper graph neural networks for high-performance property prediction in crystals and molecules](https://mlsanity.com/paper/2501.03278/) (2025)
- [Deep Learning Methods for Small Molecule Drug Discovery: A Survey](https://mlsanity.com/paper/2303.00313/) (2023)
- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [Molecular Joint Representation Learning via Multi-modal Information](https://mlsanity.com/paper/2211.14042/) (2022)
- [Learning Trajectories of Hamiltonian Systems with Neural Networks](https://mlsanity.com/paper/2204.05077/) (2022)
- [Towards Conditional Generation of Minimal Action Potential Pathways for Molecular Dynamics](https://mlsanity.com/paper/2111.14053/) (2021)
- [Equivalent Distance Geometry Error for Molecular Conformation Comparison](https://mlsanity.com/paper/2201.08714/) (2021)
- [CROP: Integrating Topological and Spatial Structures via Cross-View Prefixes for Molecular LLMs](https://mlsanity.com/paper/2508.06917/) (2025)

## Abstract (arXiv)

Well-designed molecular representations (fingerprints) are vital to combine medical chemistry and deep learning. Whereas incorporating 3D geometry of molecules (i.e. conformations) in their representations seems beneficial, current 3D algorithms are still in infancy. In this paper, we propose a novel molecular representation algorithm which preserves 3D conformations of molecules with a Molecular Hamiltonian Network (HamNet). In HamNet, implicit positions and momentums of atoms in a molecule interact in the Hamiltonian Engine following the discretized Hamiltonian equations. These implicit coordinations are supervised with real conformations with translation- & rotation-invariant losses, and further used as inputs to the Fingerprint Generator, a message-passing neural network. Experiments show that the Hamiltonian Engine can well preserve molecular conformations, and that the fingerprints generated by HamNet achieve state-of-the-art performances on MoleculeNet, a standard molecular machine learning benchmark.