# Neural Polarization: Toward Electron Density for Molecules by Extending Equivariant Networks

arXiv: https://arxiv.org/abs/2406.00441 · HTML: https://mlsanity.com/paper/2406.00441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 78 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systems](https://mlsanity.com/paper/2205.14276/) (2022)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [Beyond MD17: the reactive xxMD dataset](https://mlsanity.com/paper/2308.11155/) (2023)
- [Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery](https://mlsanity.com/paper/2205.02967/) (2022)

## Abstract (arXiv)

Recent SO(3)-equivariant models embedded a molecule as a set of single atoms fixed in the three-dimensional space, which is analogous to a ball-and-stick view. This perspective provides a concise view of atom arrangements, however, the surrounding electron density cannot be represented and its polarization effects may be underestimated. To overcome this limitation, we propose textitNeural Polarization, a novel method extending equivariant network by embedding each atom as a pair of fixed and moving points. Motivated by density functional theory, Neural Polarization represents molecules as a space-filling view which includes an electron density, in contrast with a ball-and-stick view. Neural Polarization can flexibly be applied to most type of existing equivariant models. We showed that Neural Polarization can improve prediction performances of existing models over a wide range of targets. Finally, we verified that our method can improve the expressiveness and equivariance in terms of mathematical aspects.