mlsanityData to 14 Oct 2026

Equivariant Neural Operator Learning with Graphon Convolution

arXiv 2311.10908 ↗First posted 17 Nov 2023cs.LGcited by 11

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Abstract (arXiv)

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve SE(3)-equivariance by design. From the graph spectrum view, our method can be interpreted as convolution on graphons (dense graphs with infinitely many nodes), which we term InfGCN. By leveraging both the continuous graphon structure and the discrete graph structure of the input data, our model can effectively capture the geometric information while preserving equivariance. Through extensive experiments on large-scale electron density datasets, we observed that our model significantly outperformed the current state-of-the-art architectures. Multiple ablation studies were also carried out to demonstrate the effectiveness of the proposed architecture.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 32 of its 56 references that are in the map. First posted on arXiv 17 Nov 2023.

Builds on

32 of 56 references.

References · 32

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  6. 20163D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotationcited by 1,476
  7. 2021E(n) Equivariant Graph Neural Networkscited by 965
  8. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  9. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  10. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  11. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  12. 2020Directional Message Passing for Molecular Graphscited by 561
20 more
  1. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  2. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  3. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 313
  4. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 305
  5. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 255
  6. 2022U-NO: U-shaped Neural Operatorscited by 230
  7. 2018PPFNet: Global Context Aware Local Features for Robust 3D Point Matchingcited by 181
  8. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 118
  9. 2016By-passing the Kohn-Sham equations with machine learningcited by 67
  10. 2022Generalization Analysis of Message Passing Neural Networks on Large Random Graphscited by 59
  11. 2021Equivariant Graph Neural Networks for 3D Macromolecular Structurecited by 53
  12. 2022Equivariant Point Cloud Analysis via Learning Orientations for Message Passingcited by 32
  13. 2021Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solidscited by 25
  14. 2020Graphon Filters: Graph Signal Processing in the Limitcited by 16
  15. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 14
  16. 2020DeepDFT: Neural Message Passing Network for Accurate Charge Density Predictioncited by 12
  17. 2020Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learningcited by 11
  18. 2019Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networkscited by 10
  19. 2020On the equivalence of molecular graph convolution and molecular wave function with poor basis setcited by 7
  20. 2022Prediction of the electron density of states for crystalline compounds with Atomistic Line Graph Neural Networks (ALIGNN)cited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 2; 2026: 5.

11 papers.

  1. 2025Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learningcited by 12
  2. 2025ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitalscited by 10
  3. 2024Gaussian Plane-Wave Neural Operator for Electron Density Estimationcited by 9
  4. 2024A Recipe for Charge Density Predictioncited by 9
  5. 2026Topological Neural Operatorscited by 4
  6. 2026Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blinkcited by 2
  7. 2024Physics-embedded Fourier Neural Network for Partial Differential Equationscited by 1
  8. 2026Sobek: Streaming Equivariant Tensor Product Convolutionscited by 1
  9. 2024E3STO: Orbital Inspired SE(3)-Equivariant Molecular Representation for Electron Density Predictioncited by 0
  10. 2026Complete Neural Electronic Initialization Accelerates Materials DFTcited by 0
  11. 2026Equivariant Flow Matching for Electron Density Predictioncited by 0