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Equivariant Graph Neural Networks with e3nn

Getting Started

Setting up the environment
How to use this book
Curriculum at a glance

Part I: Foundations: Symmetry, Irreps and Equivariant Operations

1. Lesson 01a: Symmetry, Equivariance and Geometric Neural Networks
2. Lesson 01b: Group Representations
3. Lesson 02a: o3.Irreps are the Type System of Equivariant Networks
4. Lesson 02b: Spherical Harmonics and the Equivariant Embedding of a Direction
5. Lesson 03a: Tensor Products and Coupling Irreps with Clebsch–Gordan Coefficients
6. Lesson 03b: Tensor Products in e3nn
7. Lesson 04: Equivariant Nonlinearities, Norm Activations and the Gate

Part II: From Operations to Networks

8. Lesson 05a: From Point Clouds to Atomistic Graphs
9. Lesson 05b: Radial Basis Functions and Smooth Cutoffs
10. Lesson 06a: The Equivariant Point Convolution (Tensor Field Networks)
11. Lesson 06b: The Tetris Example

Part III: Invariant Baselines

12. Lesson 07a: SchNet and continuous-filter convolution
13. Lesson 07b: DimeNet and the insufficiency of distance-only GNNs
14. Lesson 07c: The Rematch on Aspirin from rMD17

Part IV: State-of-the-Art Equivariant Potentials

15. Lesson 08a: Theory of NequIP as an E(3)-Equivariant Interatomic Potential
16. Lesson 08b: Block-by-Block Implementation of NequIP in e3nn
17. Lesson 08c: Training NequIP and the rMD17 Rematch

Reference

Further reading
Bibliography
Authoring style guide

Repository
Open issue

Index

By Mohammad Mostafanejad

© Copyright 2026, The Molecular Sciences Software Institute.

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Supported by the National Science Foundation under grant CHE-2136142.