This is the website for the
E(3) is the Euclidean group in dimension 3. That is the group of rotations, translations and mirror.
e3nn is a pytorch library that aims to create E(3) equivariant neural networks.
How to use the Resources
If you’d like to generally learn what
e3nn is and what it’s used for, check out some of previously recorded talks and skimming some of the papers. If you’d like to try out
e3nn, the first step is to install it.
Once you have
e3nn up and running, try out the Jupyter notebooks in e3nn_tutorial. This will give you a feel for the primary data types and classes in
e3nn. You can also read e3nn_book in parallel and dive into more rigorous math resources. This reading will be helpful for parsing even the most techincal parts of the relevant papers.
If you want to talk to other folks using
e3nn, you are most welcome to join our recurring monthly meetings which are shown in the e3nn calendar and our Slack.
We want to help eliminate any bottlenecks in making Euclidean equivariant neural networks and
e3nn accessible to a broad audience, especially scientists whose primary expertise is not machine learning. If you have an application in mind but not sure how to structure a network around it or other questions not satisfied by this page’s resources, feel free to reach out to Tess (
Be careful to install a version of
torch_geometric that matches the same CUDA version that your
torch installation uses (this is general advice and not
The full instructions for installing
e3nn can be found here.
The documentation is here
Math that’s good to know
e3nn makes use of group theory and representation theory. You don’t need to be knowledgeable on these topics to start using
e3nn but it might be useful to have some relevant resources handy. Some of our favorite resources are:
e3nn_book [in progress]
We are currently in the progress of compiling a more user-friendly introduction to the core concepts used in
Some previous recorded talks on
2020/11 Euclidean Neural Networks for Physics ∩ ML, November 18, 2020. (slides // video)
2020/09 Unintended Features of E(3)NNs, Workshop on Equivariance and Data Augmentation (video // slides), University of Pennsylvania, September 4, 2020
2020/09 Lecture on Symmetry and Equivariance in ML, Berkeley Lab Deep Learning School (video // slides), Berkeley Lab, September 3, 2020.
2020/07 Neural Networks with Euclidean Symmetry for Physical Sciences, 1st Workshop on Scientific-Driven Deep Learning (SciDL) (video // slides), July 1, 2020
2020/01 An autoencoder for discrete geometry, Applied Machine Learning Days – AI and the Molecular World (video), EPFL, January 27-28, 2020, Lausanne, Switzerland
2019/12 Euclidean Neural Networks for Emulating Ab Initio Calculations and Generating Atomic Geometries, eScience Institute Seminar (video), University of Washington, Seattle, WA
2019/09 Euclidean Neural Networks for Emulating Ab Initio Calculations and Generating Atomic Geometries, Workshop I: From Passive to Active: Generative and Reinforcement Learning with Physics, (video // slides), IPAM at UCLA, Los Angeles, CA
A poster overview of the
(in reserve chronological order)
- 2021/01 SE(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials
- Simon Batzner, Tess E. Smidt, Lixin Sun, Jonathan P. Mailoa, Mordechai Kornbluth, Nicola Molinari, Boris Kozinsky
- An equivariant Machine Learning Interatomic Potential that not obtains SOTA on MD-17 and outperforms existing potentials with up to 1000x fewer data.
- 2020/10 On the Universality of Rotation Equivariant Point Cloud Networks
- Nadav Dym, Haggai Maron
- Proves the expressivity of rotation equivariant neural networks.
- 2020/09 Direct prediction of phonon density of states with Euclidean neural network
- Zhantao Chen, Nina Andrejevic, Tess Smidt, Zhiwei Ding, Yen-Ting Chi, Quynh T. Nguyen, Ahmet Alatas, Jing Kong, Mingda Li
e3nn is used to predict phonon density of states (DOS) from crystal structure. Trained network is used to identify materials with high specific heat.
- 2020/09 Euclidean Symmetry and Equivariance in Machine Learning
- Tess E. Smidt
- A mini review on invariant vs. equivariant ML models.
- 2020/08 Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties
- Benjamin Kurt Miller, Mario Geiger, Tess E. Smidt, Frank Noé
- Includes benchmark of
e3nn on QM9.
- 2020/07 Finding Symmetry Breaking Order Parameters with Euclidean Neural Networks (code)
- Tess E. Smidt, Mario Geiger, Benjamin Kurt Miller
- Demonstrates how to use
e3nn to perform a symmetry analysis to resolve order parameters for 2nd order phase transitions.
- 2020/06 Hierarchical, rotation-equivariant neural networks to predict the structure of protein complexes
- Stephan Eismann, Raphael J.L. Townshend, Nathaniel Thomas, Milind Jagota, Bowen Jing, Ron Dror
- 2020/06 SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks
- Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, Max Welling
- 2019/06 Cormorant
- Brandon Anderson, Truong-Son Hy, Risi Kondor
- Introduces n-body convolutions.
- 2018/07 3D Steerable CNNs*
- Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, Taco Cohen
- 2018/06 Clebsch-Gordan Networks*
- Risi Kondor, Zhen Lin, Shubhendu Trivedi
- 2018/02 Tensor Field Networks* (code)
- Nathaniel Thomas, Tess Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, Patrick Riley
*indicates foundational paper in the development of Euclidean neural networks.
If there are any papers that you think should be on this list but are missing, please email Tess
firstname.lastname@example.org with a citation and description that matches the examples above.
e3nn developers and several collaborators discuss ideas and help each other out with projects via Slack. If you’d like to join the Slack, please send an email to Tess
Recurring Meetings / Events
e3nn has two recurring monthly meetings in addition to other events on our calendar.
- A monthly developers / collaboration 1.5 hour meeting on the first Wednesday of every month (typically) at 10 am Pacific Time. We typically go around and each give a brief update on what we’ve been working on and if there are any difficulties we are running into.
- A monthly tutorials / documentation hackathon on the second Wednesday of every month starting at 10 am Pacific Time and ending around 6 pm Pacific Time. This is a great opportunity to ask questions.
Everyone is welcome to join these meetings – yes, that means you! The meeting links are in the calendar events show below. Feel free to reach out to
email@example.com to introduce yourself if you are new to joining the meetings.
To get help with a question or code bug, please follow this link.
To get involved with the development and improvement of
e3nn, please follow this link.
with Upcoming Tutorials / Meetings / Hackathons
(aka the people answering pull-requests)
Collaborators and Contributors
- Josh Rackers
- Thomas Hardin
- Simon Batzner
- Boris Kozinsky
- Eugene Kwan
- Albert Musaelian
- Frank Noé
- Claire West
- Zhantao Chem
- Nina Andrejevic
- Mingda Li