# FAENet: Frame Averaging Equivariant GNN for Materials Modeling

arXiv: https://arxiv.org/abs/2305.05577 · HTML: https://mlsanity.com/paper/2305.05577/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 61 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 30 of 39)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [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)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [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)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://mlsanity.com/paper/2103.01436/) (2021)
- [Geometrically Equivariant Graph Neural Networks: A Survey](https://mlsanity.com/paper/2202.07230/) (2022)

## Built on by (most cited first, 30 of 73)

- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Equivariant Frames and the Impossibility of Continuous Canonicalization](https://mlsanity.com/paper/2402.16077/) (2024)
- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (2023)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [A Canonicalization Perspective on Invariant and Equivariant Learning](https://mlsanity.com/paper/2405.18378/) (2024)
- [Application-Driven Innovation in Machine Learning](https://mlsanity.com/paper/2403.17381/) (2024)
- [Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency](https://mlsanity.com/paper/2406.07598/) (2024)
- [Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fields](https://mlsanity.com/paper/2403.09549/) (2024)
- [Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?](https://mlsanity.com/paper/2410.11443/) (2024)
- [Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding](https://mlsanity.com/paper/2403.11686/) (2024)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modeling](https://mlsanity.com/paper/2309.05934/) (2023)
- [Probing the effects of broken symmetries in machine learning](https://mlsanity.com/paper/2406.17747/) (2024)
- [Relaxed Equivariance via Multitask Learning](https://mlsanity.com/paper/2410.17878/) (2024)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Efficient Equivariant Transfer Learning from Pretrained Models](https://mlsanity.com/paper/2305.09900/) (2023)
- [On the Completeness of Invariant Geometric Deep Learning Models](https://mlsanity.com/paper/2402.04836/) (2024)
- [Predicting solvation free energies with an implicit solvent machine learning potential](https://mlsanity.com/paper/2406.00183/) (2024)
- [ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitals](https://mlsanity.com/paper/2503.08305/) (2025)
- [Beyond Sequence: Impact of Geometric Context for RNA Property Prediction](https://mlsanity.com/paper/2410.11933/) (2024)
- [Improved Canonicalization for Model Agnostic Equivariance](https://mlsanity.com/paper/2405.14089/) (2024)
- [Object-Centric Temporal Consistency via Conditional Autoregressive Inductive Biases](https://mlsanity.com/paper/2410.15728/) (2024)
- [Stiefel Flow Matching for Moment-Constrained Structure Elucidation](https://mlsanity.com/paper/2412.12540/) (2024)
- [Learning Inter-Atomic Potentials without Explicit Equivariance](https://mlsanity.com/paper/2510.00027/) (2025)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [Stress-Testing Multimodal Foundation Models for Crystallographic Reasoning](https://mlsanity.com/paper/2506.13051/) (2025)
- [Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networks](https://mlsanity.com/paper/2508.19071/) (2025)
- [LeMat-Traj: A Scalable and Unified Dataset of Materials Trajectories for Atomistic Modeling](https://mlsanity.com/paper/2508.20875/) (2025)
- [Scaling Laws and Symmetry, Evidence from Neural Force Fields](https://mlsanity.com/paper/2510.09768/) (2025)

## Abstract (arXiv)

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they enforce symmetries via the model architecture, which often reduces their expressivity, scalability and comprehensibility. In this paper, we introduce (1) a flexible framework relying on stochastic frame-averaging (SFA) to make any model E(3)-equivariant or invariant through data transformations. (2) FAENet: a simple, fast and expressive GNN, optimized for SFA, that processes geometric information without any symmetrypreserving design constraints. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X). A package implementation is available at https://faenet.readthedocs.io.