# Stable and Accurate Orbital-Free DFT Powered by Machine Learning

arXiv: https://arxiv.org/abs/2503.00443 · HTML: https://mlsanity.com/paper/2503.00443/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 89 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Benchmarking Graphormer on Large-Scale Molecular Modeling Datasets](https://mlsanity.com/paper/2203.04810/) (2022)
- [TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentials](https://mlsanity.com/paper/2306.06482/) (2023)
- [Equivariant Point Cloud Analysis via Learning Orientations for Message Passing](https://mlsanity.com/paper/2203.14486/) (2022)
- [Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passing](https://mlsanity.com/paper/2405.15389/) (2024)
- [Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning](https://mlsanity.com/paper/2309.16578/) (2023)
- [KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory](https://mlsanity.com/paper/2305.13316/) (2023)

## Abstract (arXiv)

Hohenberg and Kohn have proven that the electronic energy and the one-particle electron density can, in principle, be obtained by minimizing an energy functional with respect to the density. While decades of theoretical work have produced increasingly faithful approximations to this elusive exact energy functional, their accuracy is still insufficient for many applications, making it reasonable to try and learn it empirically. Using rotationally equivariant atomistic machine learning, we obtain for the first time a density functional that, when applied to the organic molecules in QM9, yields energies with chemical accuracy relative to the Kohn-Sham reference while also converging to meaningful electron densities. Augmenting the training data with densities obtained from perturbed potentials proved key to these advances. This work demonstrates that machine learning can play a crucial role in narrowing the gap between theory and the practical realization of Hohenberg and Kohn's vision, paving the way for more efficient calculations in large molecular systems.