mlsanityData to 7 Oct 2026

Equivariant Graph Mechanics Networks with Constraints

arXiv 2203.06442 ↗First posted 12 Mar 2022cs.LGcited by 67

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Abstract (arXiv)

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and commonly geometrically-constrained. Current methods, particularly the ones based on equivariant Graph Neural Networks (GNNs), have targeted on the first two challenges but remain immature for constrained systems. In this paper, we propose Graph Mechanics Network (GMN) which is combinatorially efficient, equivariant and constraint-aware. The core of GMN is that it represents, by generalized coordinates, the forward kinematics information (positions and velocities) of a structural object. In this manner, the geometrical constraints are implicitly and naturally encoded in the forward kinematics. Moreover, to allow equivariant message passing in GMN, we have developed a general form of orthogonality-equivariant functions, given that the dynamics of constrained systems are more complicated than the unconstrained counterparts. Theoretically, the proposed equivariant formulation is proved to be universally expressive under certain conditions. Extensive experiments support the advantages of GMN compared to the state-of-the-art GNNs in terms of prediction accuracy, constraint satisfaction and data efficiency on the simulated systems consisting of particles, sticks and hinges, as well as two real-world datasets for molecular dynamics prediction and human motion capture.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). Builds on 19 of its 26 references that are in the map. First posted on arXiv 12 Mar 2022.

Builds on

19 of 26 references.

References · 19

  1. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  4. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  5. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  6. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  7. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 503
  8. 2018Neural Relational Inference for Interacting Systemscited by 339
  9. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  10. 2018Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluidscited by 219
  11. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  12. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
7 more
  1. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  2. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
  3. 2020LieTransformer: Equivariant self-attention for Lie Groupscited by 100
  4. 2018Flexible Neural Representation for Physics Predictioncited by 91
  5. 2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
  6. 2020Learning Physical Constraints with Neural Projectionscited by 19
  7. 2020Scalable Graph Networks for Particle Simulationscited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 18; 2024: 21; 2025: 14; 2026: 5.

67 papers.

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  1. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  2. 2022Conditional Antibody Design as 3D Equivariant Graph Translationcited by 75
  3. 2023Clifford Group Equivariant Neural Networkscited by 54
  4. 2023End-to-End Full-Atom Antibody Designcited by 48
  5. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  6. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 38
  7. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 37
  8. 2022E3Bind: An End-to-End Equivariant Network for Protein-Ligand Dockingcited by 35
  9. 2023AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodiescited by 35
  10. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  11. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  12. 2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulationscited by 24
38 more
  1. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22
  2. 2022Graph Neural Networks for Moleculescited by 21
  3. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  4. 2023Generalist Equivariant Transformer Towards 3D Molecular Interaction Learningcited by 18
  5. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  6. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  7. 2022Geometry-Complete Perceptron Networks for 3D Molecular Graphscited by 15
  8. 2023EquiPocket: an E(3)-Equivariant Geometric Graph Neural Network for Ligand Binding Site Predictioncited by 15
  9. 2024Graph Neural PDE Solvers with Conservation and Similarity-Equivariancecited by 15
  10. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14
  11. 2024Geometric Trajectory Diffusion Modelscited by 13
  12. 2024Relaxed Equivariance via Multitask Learningcited by 13
  13. 2023Spatial Attention Kinetic Networks with E(n)-Equivariancecited by 11
  14. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  15. 2023Subequivariant Graph Reinforcement Learning in 3D Environmentscited by 10
  16. 2023Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networkscited by 10
  17. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  18. 2025Large Language-Geometry Model: When LLM meets Equivariancecited by 10
  19. 2022Finding Diverse and Predictable Subgraphs for Graph Domain Generalizationcited by 9
  20. 2023Cross-Gate MLP with Protein Complex Invariant Embedding is A One-Shot Antibody Designercited by 8
  21. 2023Latent Field Discovery In Interacting Dynamical Systems With Neural Fieldscited by 7
  22. 2023Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamicscited by 6
  23. 2024GeoMFormer: A General Architecture for Geometric Molecular Representation Learningcited by 6
  24. 2024DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equationcited by 6
  25. 2025Fast and Distributed Equivariant Graph Neural Networks by Virtual Node Learningcited by 6
  26. 2024A Clifford Algebraic Approach to E(n)-Equivariant High-order Graph Neural Networkscited by 5
  27. 2024DEL: Discrete Element Learner for Learning 3D Particle Dynamics with Neural Renderingcited by 4
  28. 2025Natural Language-Assisted Multi-modal Medication Recommendationcited by 4
  29. 2023Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systemscited by 3
  30. 2024E(n) Equivariant Message Passing Cellular Networkscited by 3
  31. 2025Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systemscited by 3
  32. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  33. 2023Graph Neural Stochastic Differential Equations for Learning Brownian Dynamicscited by 2
  34. 2023Geometric Deep Learning for Structure-Based Drug Design: A Surveycited by 2
  35. 2024Subequivariant Reinforcement Learning Framework for Coordinated Motion Controlcited by 2
  36. 2024HeMeNet: Heterogeneous Multichannel Equivariant Network for Protein Multitask Learningcited by 2
  37. 2024Subequivariant Reinforcement Learning in 3D Multi-Entity Physical Environmentscited by 2
  38. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2

50 most cited of 67 All 67 (JSON)