# E3STO: Orbital Inspired SE(3)-Equivariant Molecular Representation for Electron Density Prediction

arXiv: https://arxiv.org/abs/2410.06119 · HTML: https://mlsanity.com/paper/2410.06119/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [DeepDFT: Neural Message Passing Network for Accurate Charge Density Prediction](https://mlsanity.com/paper/2011.03346/) (2020)
- [Equivariant Neural Operator Learning with Graphon Convolution](https://mlsanity.com/paper/2311.10908/) (2023)
- [Gaussian Plane-Wave Neural Operator for Electron Density Estimation](https://mlsanity.com/paper/2402.04278/) (2024)
- [A Recipe for Charge Density Prediction](https://mlsanity.com/paper/2405.19276/) (2024)

## Abstract (arXiv)

Electron density prediction stands as a cornerstone challenge in molecular systems, pivotal for various applications such as understanding molecular interactions and conducting precise quantum mechanical calculations. However, the scaling of density functional theory (DFT) calculations is prohibitively expensive. Machine learning methods provide an alternative, offering efficiency and accuracy. We introduce a novel SE(3)-equivariant architecture, drawing inspiration from Slater-Type Orbitals (STO), to learn representations of molecular electronic structures. Our approach offers an alternative functional form for learned orbital-like molecular representation. We showcase the effectiveness of our method by achieving SOTA prediction accuracy of molecular electron density with 30-70% improvement over other work on Molecular Dynamics data.