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V2Rho-FNO: Fourier Neural Operator for Electronic Density Prediction

Yingdi Jin, Xinming Qin, Ruichen Liu, Jie Liu, Zhenyu Li, Jinlong Yang

Abstract

Density functional theory (DFT) is a cornerstone of computational chemistry and materials science, but its computational cost limits its use in large-scale and high-throughput applications. While machine learning has accelerated energy prediction for specific molecular classes, transferable prediction of electron density across diverse chemical spaces remains challenging. Here, we present a universal framework based on Fourier Neural Operators (FNOs) that directly learns the mapping from external potentials to electron density distributions. Unlike conventional approaches that rely on explicit atomic orbitals, basis sets, or handcrafted descriptors, the proposed method captures global electronic interactions and long-range correlations through operator learning in the spatial-frequency domain. Trained on datasets spanning multiple elements and molecular geometries, the model achieves zero-shot generalization to entirely unseen molecular systems and accurately predicts their electron densities without retraining. This transferability arises from the intrinsic ability of FNOs to represent global structure in continuous fields. Our work establishes neural operator learning as a promising route for fast, accurate, and transferable electronic structure prediction, with potential applications in high-throughput screening and chemical space exploration.

V2Rho-FNO: Fourier Neural Operator for Electronic Density Prediction

Abstract

Density functional theory (DFT) is a cornerstone of computational chemistry and materials science, but its computational cost limits its use in large-scale and high-throughput applications. While machine learning has accelerated energy prediction for specific molecular classes, transferable prediction of electron density across diverse chemical spaces remains challenging. Here, we present a universal framework based on Fourier Neural Operators (FNOs) that directly learns the mapping from external potentials to electron density distributions. Unlike conventional approaches that rely on explicit atomic orbitals, basis sets, or handcrafted descriptors, the proposed method captures global electronic interactions and long-range correlations through operator learning in the spatial-frequency domain. Trained on datasets spanning multiple elements and molecular geometries, the model achieves zero-shot generalization to entirely unseen molecular systems and accurately predicts their electron densities without retraining. This transferability arises from the intrinsic ability of FNOs to represent global structure in continuous fields. Our work establishes neural operator learning as a promising route for fast, accurate, and transferable electronic structure prediction, with potential applications in high-throughput screening and chemical space exploration.
Paper Structure (35 sections, 12 equations, 9 figures)

This paper contains 35 sections, 12 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Results
  3. Generalization under different training--test relations
  4. (a) Interpolation along molecular dynamics trajectories.
  5. (b) Random molecular generalization within QM9.
  6. (c) Element-level extrapolation to fluorine-containing molecules.
  7. Resolution transfer across training--test regimes
  8. Discussion
  9. Operator interpretation via nonlocal density response.
  10. Why a potential-field input is natural for neural operators.
  11. Origin of transferability across local bonding environments and chemical elements
  12. Resolution transfer and spectral zero-padding in Fourier neural operators
  13. Relation to recent neural-operator-based density models
  14. Outlook
  15. Methods
  16. ...and 20 more sections

Figures (9)

  • Figure 1: H2O correlation analysis.
  • Figure 2: Bonding environments extrapolation: training on the first 5,000 molecules from QM9, and evaluation on molecules whose local bonding environments are not present in the training set, followed by correlation and error analysis between predicted densities and DFT-calculated densities.
  • Figure 3: bonding enviroments generation:Comparison between predicted density and DFT-calculated density
  • Figure 4: Element-wise extrapolation of model-predicted densities: training on the remaining systems after excluding fluorine-containing groups from the first 5,000 molecules in QM9, followed by extrapolation to fluorine-containing molecules for prediction, and correlation and error analysis between predicted densities and DFT-calculated densities.
  • Figure 5: Element-wise extrapolation: Comparison between predicted density and DFT-calculated density
  • ...and 4 more figures