mlsanityData to 14 Oct 2026

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

arXiv 2312.07511 ↗First posted 12 Dec 2023cs.LG cs.AI q-bio.QMcited by 68

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Abstract (arXiv)

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

Key facts. Cited by 68 papers in the map (data through 14 Oct 2026). Builds on 92 of its 214 references that are in the map. First posted on arXiv 12 Dec 2023.

Builds on

92 of 214 references.

References · 92

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38 more
  1. 2021E(n) Equivariant Graph Neural Networkscited by 965
  2. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  3. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 754
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  20. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
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50 most cited of 92 All 92 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 31; 2025: 25; 2026: 12.

68 papers.

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  1. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  2. 2024Open Materials 2024 (OMat24) Inorganic Materials Dataset and Modelscited by 52
  3. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 51
  4. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 43
  5. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 36
  6. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  7. 2024The dark side of the forces: assessing non-conservative force models for atomistic machine learningcited by 24
  8. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 23
  9. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 19
  10. 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
  11. 2024MatExpert: Decomposing Materials Discovery by Mimicking Human Expertscited by 18
  12. 2024Foundational Large Language Models for Materials Researchcited by 18
38 more
  1. 2024Evaluating representation learning on the protein structure universecited by 16
  2. 2024TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulationscited by 15
  3. 2024Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passingcited by 15
  4. 2025Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systemscited by 14
  5. 2024Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passingcited by 13
  6. 2024Less can be more for predicting properties with large language modelscited by 11
  7. 2026Pushing the limits of unconstrained machine-learned interatomic potentialscited by 11
  8. 2025How simple can you go? An off-the-shelf transformer approach to molecular dynamicscited by 10
  9. 2024A Recipe for Charge Density Predictioncited by 9
  10. 2024Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networkscited by 9
  11. 2024AdsorbDiff: Adsorbate Placement via Conditional Denoising Diffusioncited by 8
  12. 2024Improved Canonicalization for Model Agnostic Equivariancecited by 7
  13. 2024Future Directions in the Theory of Graph Machine Learningcited by 6
  14. 2025Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learningcited by 6
  15. 2025UniFFBench: Evaluating Universal Machine Learning Force Fields Against Experimental Measurementscited by 6
  16. 2025DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomoleculescited by 5
  17. 2025Molecular Machine Learning in Chemical Process Designcited by 5
  18. 2024Equivariant Neural Tangent Kernelscited by 4
  19. 2025Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networkscited by 4
  20. 2025LeMat-Traj: A Scalable and Unified Dataset of Materials Trajectories for Atomistic Modelingcited by 4
  21. 2025CrystalGym: A New Benchmark for Materials Discovery Using Reinforcement Learningcited by 4
  22. 2024AMARO: All Heavy-Atom Transferable Neural Network Potentials of Protein Thermodynamicscited by 3
  23. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  24. 2025Catalyst GFlowNet for electrocatalyst design: A hydrogen evolution reaction case studycited by 3
  25. 2024Understanding Biology in the Age of Artificial Intelligencecited by 2
  26. 2024Interpolation and differentiation of alchemical degrees of freedom in machine learning interatomic potentialscited by 2
  27. 2024Deconstructing equivariant representations in molecular systemscited by 2
  28. 2024Bridging Geometric States via Geometric Diffusion Bridgecited by 2
  29. 2025Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networkscited by 2
  30. 2025Fast, Modular, and Differentiable Framework for Machine Learning-Enhanced Molecular Simulationscited by 2
  31. 2025Understanding Generalization in Node and Link Predictioncited by 2
  32. 2026An SO(3)-equivariant reciprocal-space neural potential for long-range interactionscited by 2
  33. 2026XANE(3): An E(3)-Equivariant Graph Neural Network for Accurate Prediction of XANES Spectra from Atomic Structurescited by 2
  34. 2024On the Fourier analysis in the SO(3) space : EquiLoPO Networkcited by 1
  35. 2025QuantumBind-RBFE: Accurate Relative Binding Free Energy Calculations Using Neural Network Potentialscited by 1
  36. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  37. 2025Solar-GECO: Perovskite Solar Cell Property Prediction with Geometric-Aware Co-Attentioncited by 1
  38. 2026AceFF: A State-of-the-Art Machine Learning Potential for Small Moleculescited by 1

50 most cited of 68 All 68 (JSON)