# Learning local and semi-local density functionals from exact exchange-correlation potentials and energies

arXiv: https://arxiv.org/abs/2409.06498 · HTML: https://mlsanity.com/paper/2409.06498/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 89 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 3 of 3)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Transferable Recommender Approach for Selecting the Best Density Functional Approximations in Chemical Discovery](https://mlsanity.com/paper/2207.10747/) (2022)
- [Machine learning for accuracy in density functional approximations](https://mlsanity.com/paper/2311.00196/) (2023)

## Built on by (most cited first, 3 of 3)

- [Accurate and scalable exchange-correlation with deep learning](https://mlsanity.com/paper/2506.14665/) (2025)
- [Derivative Informed Learning of Exchange-Correlation Functionals](https://mlsanity.com/paper/2606.04279/) (2026)
- [Coupled Cluster con M=oLe: Molecular Orbital Learning for Neural Wavefunctions](https://mlsanity.com/paper/2602.20232/) (2026)

## Abstract (arXiv)

Finding accurate exchange-correlation (XC) functionals remains the defining challenge in density functional theory (DFT). Despite 40 years of active development, the desired chemical accuracy is still elusive with existing functionals. We present a data-driven pathway to learn the XC functionals by utilizing the exact density, XC energy, and XC potential. While the exact densities are obtained from accurate configuration interaction (CI), the exact XC energies and XC potentials are obtained via inverse DFT calculations on the CI densities. We demonstrate how simple neural network (NN) based local density approximation (LDA) and generalized gradient approximation (GGA), trained on just five atoms and two molecules, provide remarkable improvement in total energies, densities, atomization energies, and barrier heights for hundreds of molecules outside the training set. Particularly, the NN-based GGA functional attains similar accuracy as the higher rung SCAN meta-GGA, highlighting the promise of using the XC potential in modeling XC functionals. We expect this approach to pave the way for systematic learning of increasingly accurate and sophisticated XC functionals.