mlsanityData to 7 Oct 2026

Gaussian Plane-Wave Neural Operator for Electron Density Estimation

arXiv 2402.04278 ↗First posted 5 Feb 2024physics.chem-ph cs.LGcited by 8

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Abstract (arXiv)

This work studies machine learning for electron density prediction, which is fundamental for understanding chemical systems and density functional theory (DFT) simulations. To this end, we introduce the Gaussian plane-wave neural operator (GPWNO), which operates in the infinite-dimensional functional space using the plane-wave and Gaussian-type orbital bases, widely recognized in the context of DFT. In particular, both high- and low-frequency components of the density can be effectively represented due to the complementary nature of the two bases. Extensive experiments on QM9, MD, and material project datasets demonstrate GPWNO's superior performance over ten baselines.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 15 of its 52 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

15 of 52 references.

References · 15

  1. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  5. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  6. 2020Directional Message Passing for Molecular Graphscited by 556
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  8. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  9. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  10. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  11. 2021Factorized Fourier Neural Operatorscited by 237
  12. 2022e3nn: Euclidean Neural Networkscited by 171
3 more
  1. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  2. 2020DeepDFT: Neural Message Passing Network for Accurate Charge Density Predictioncited by 12
  3. 2023Equivariant Neural Operator Learning with Graphon Convolutioncited by 10

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Cited by year (2026 to 7 Oct)

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

8 papers.

  1. 2025ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitalscited by 9
  2. 2024A Recipe for Charge Density Predictioncited by 8
  3. 2026Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operatorscited by 6
  4. 2025SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Samplingcited by 1
  5. 2026Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blinkcited by 1
  6. 2024E3STO: Orbital Inspired SE(3)-Equivariant Molecular Representation for Electron Density Predictioncited by 0
  7. 2026Euclidean Fourier Neural Operatorscited by 0
  8. 2026Complete Neural Electronic Initialization Accelerates Materials DFTcited by 0