# E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials

arXiv: https://arxiv.org/abs/2101.03164 · HTML: https://mlsanity.com/paper/2101.03164/

## Key facts

- Cited by 708 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 67 references that are in the map.
- First posted on arXiv 8 Jan 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials](https://mlsanity.com/paper/1803.01588/) (2018)
- [Fast Neural Network Approach for Direct Covariant Forces Prediction in Complex Multi-Element Extended Systems](https://mlsanity.com/paper/1905.02791/) (2019)
- [Geometric Prediction: Moving Beyond Scalars](https://mlsanity.com/paper/2006.14163/) (2020)

## Built on by (most cited first, 30 of 708)

- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [Broken Neural Scaling Laws](https://mlsanity.com/paper/2210.14891/) (2022)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (2022)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [14 Examples of How LLMs Can Transform Materials Science and Chemistry: A Reflection on a Large Language Model Hackathon](https://mlsanity.com/paper/2306.06283/) (2023)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials](https://mlsanity.com/paper/2209.10702/) (2022)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)

## Abstract (arXiv)

This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales.