# Facet: highly efficient E(3)-equivariant networks for interatomic potentials

arXiv: https://arxiv.org/abs/2509.08418 · HTML: https://mlsanity.com/paper/2509.08418/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 51 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Prodigy: An Expeditiously Adaptive Parameter-Free Learner](https://mlsanity.com/paper/2306.06101/) (2023)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domains](https://mlsanity.com/paper/2410.24169/) (2024)
- [Matbench Discovery -- A framework to evaluate machine learning crystal stability predictions](https://mlsanity.com/paper/2308.14920/) (2023)
- [Scalable deeper graph neural networks for high-performance materials property prediction](https://mlsanity.com/paper/2109.12283/) (2021)
- [chemtrain-deploy: A parallel and scalable framework for machine learning potentials in million-atom MD simulations](https://mlsanity.com/paper/2506.04055/) (2025)
- [DistMLIP: A Distributed Inference Platform for Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2506.02023/) (2025)
- [Crystal structure prediction using neural network potential and age-fitness Pareto genetic algorithm](https://mlsanity.com/paper/2309.06710/) (2023)
- [A Review of DeepSeek Models' Key Innovative Techniques](https://mlsanity.com/paper/2503.11486/) (2025)
- [FastCHGNet: Training one Universal Interatomic Potential to 1.5 Hours with 32 GPUs](https://mlsanity.com/paper/2412.20796/) (2024)
- [Polymorphism Crystal Structure Prediction with Adaptive Space Group Diversity Control](https://mlsanity.com/paper/2506.11332/) (2025)

## Abstract (arXiv)

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.