mlsanityData to 7 Oct 2026

MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields

arXiv 2206.07697 ↗First posted 15 Jun 2022stat.ML cond-mat.mtrl-sci cs.LGcited by 467

Not on the map. Why?

Abstract (arXiv)

Creating fast and accurate force fields is a long-standing challenge in computational chemistry and materials science. Recently, several equivariant message passing neural networks (MPNNs) have been shown to outperform models built using other approaches in terms of accuracy. However, most MPNNs suffer from high computational cost and poor scalability. We propose that these limitations arise because MPNNs only pass two-body messages leading to a direct relationship between the number of layers and the expressivity of the network. In this work, we introduce MACE, a new equivariant MPNN model that uses higher body order messages. In particular, we show that using four-body messages reduces the required number of message passing iterations to just two, resulting in a fast and highly parallelizable model, reaching or exceeding state-of-the-art accuracy on the rMD17, 3BPA, and AcAc benchmark tasks. We also demonstrate that using higher order messages leads to an improved steepness of the learning curves.

Key facts. Cited by 467 papers in the map (data through 7 Oct 2026). Builds on 25 of its 53 references that are in the map. First posted on arXiv 15 Jun 2022.

Builds on

25 of 53 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  4. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  5. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  6. 2016Group Equivariant Convolutional Networkscited by 1,154
  7. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  8. 2021E(n) Equivariant Graph Neural Networkscited by 951
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  11. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  12. 2017Deep Learning Scaling is Predictable, Empiricallycited by 556
13 more
  1. 2020Directional Message Passing for Molecular Graphscited by 556
  2. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  3. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  4. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  5. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  6. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  7. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  8. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  9. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  10. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  11. 2018N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentialscited by 42
  12. 2017Hierarchical modeling of molecular energies using a deep neural networkcited by 37
  13. 2022Unified theory of atom-centered representations and message-passing machine-learning schemescited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 12; 2023: 59; 2024: 108; 2025: 135; 2026: 153.

467 papers.

Sort:

By area:

  1. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  2. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  3. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  4. 2022SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentialscited by 80
  5. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
  6. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  7. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  8. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  9. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  10. 2024Orb: A Fast, Scalable Neural Network Potentialcited by 63
  11. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  12. 2025Position: Graph Learning Will Lose Relevance Due To Poor Benchmarkscited by 52
38 more
  1. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generationcited by 50
  2. 2024Open Materials 2024 (OMat24) Inorganic Materials Dataset and Modelscited by 50
  3. 2024Does equivariance matter at scale?cited by 49
  4. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  5. 2023Geometric Algebra Transformercited by 46
  6. 2023OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentialscited by 44
  7. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 41
  8. 2022Structure-based drug design with geometric deep learningcited by 40
  9. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  10. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  11. 2023From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Predictioncited by 39
  12. 20233D molecule generation by denoising voxel gridscited by 38
  13. 2023Geometric Clifford Algebra Networkscited by 37
  14. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  15. 2023Towards Foundational Models for Molecular Learning on Large-Scale Multi-Task Datasetscited by 37
  16. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 35
  17. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
  18. 2023Matbench Discovery -- A framework to evaluate machine learning crystal stability predictionscited by 34
  19. 2023Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic sizecited by 33
  20. 2025CASCADE: Cumulative Agentic Skill Creation through Autonomous Development and Evolutioncited by 33
  21. 2024Cartesian atomic cluster expansion for machine learning interatomic potentialscited by 31
  22. 2022SchNetPack 2.0: A neural network toolbox for atomistic machine learningcited by 29
  23. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 28
  24. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  25. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  26. 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
  27. 2024Diffusion Models in textitDe Novo Drug Designcited by 26
  28. 2024Latent Ewald summation for machine learning of long-range interactionscited by 26
  29. 2025Open Materials Generation with Stochastic Interpolantscited by 26
  30. 2023Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencecited by 25
  31. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  32. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  33. 2025A practical guide to machine learning interatomic potentials -- Status and futurecited by 24
  34. 2023Uncovering Neural Scaling Laws in Molecular Representation Learningcited by 23
  35. 2024Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groupscited by 23
  36. 2024The dark side of the forces: assessing non-conservative force models for atomistic machine learningcited by 23
  37. 2023Is Distance Matrix Enough for Geometric Deep Learning?cited by 22
  38. 2023Navigating protein landscapes with a machine-learned transferable coarse-grained modelcited by 22

50 most cited of 467 All 467 (JSON)