# Accurate and scalable exchange-correlation with deep learning

arXiv: https://arxiv.org/abs/2506.14665 · HTML: https://mlsanity.com/paper/2506.14665/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 153 references that are in the map.
- First posted on arXiv 17 Jun 2025.

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

- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Transition1x -- a Dataset for Building Generalizable Reactive Machine Learning Potentials](https://mlsanity.com/paper/2207.12858/) (2022)
- [Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics](https://mlsanity.com/paper/2009.08551/) (2020)
- [Learning the exchange-correlation functional from nature with fully differentiable density functional theory](https://mlsanity.com/paper/2102.04229/) (2021)
- [VN-EGNN: E(3)-Equivariant Graph Neural Networks with Virtual Nodes Enhance Protein Binding Site Identification](https://mlsanity.com/paper/2404.07194/) (2024)
- [3DReact: Geometric deep learning for chemical reactions](https://mlsanity.com/paper/2312.08307/) (2023)
- [Learning Equivariant Non-Local Electron Density Functionals](https://mlsanity.com/paper/2410.07972/) (2024)
- [Highly Accurate Real-space Electron Densities with Neural Networks](https://mlsanity.com/paper/2409.01306/) (2024)
- [How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?](https://mlsanity.com/paper/2110.14846/) (2021)
- [Learning local and semi-local density functionals from exact exchange-correlation potentials and energies](https://mlsanity.com/paper/2409.06498/) (2024)
- [On the Efficient Evaluation of the Exchange Correlation Potential on Graphics Processing Unit Clusters](https://mlsanity.com/paper/2007.03143/) (2020)

## Built on by (most cited first, 8 of 8)

- [FragmentFlow: Scalable Transition State Generation for Large Molecules](https://mlsanity.com/paper/2602.02310/) (2026)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [Learning Minimal Representations of Fermionic Ground States](https://mlsanity.com/paper/2512.11767/) (2025)
- [Coupled Cluster con M=oLe: Molecular Orbital Learning for Neural Wavefunctions](https://mlsanity.com/paper/2602.20232/) (2026)
- [When do machine-learned exchange-correlation improvements inherit into density-functional tight binding?](https://mlsanity.com/paper/2608.14875/) (2026)
- [Coupled-cluster molecular properties across the main group that extrapolate beyond training size](https://mlsanity.com/paper/2608.18346/) (2026)
- [A strategic roadmap for an atomistic machine-learning ecosystem](https://mlsanity.com/paper/2609.39090/) (2026)
- [Physics-Aligned Electronic Ground-State Learning Improves Generalization](https://mlsanity.com/paper/2610.10298/) (2026)

## Abstract (arXiv)

Density Functional Theory (DFT) underpins much of modern computational chemistry and materials science. Yet, the reliability of DFT-derived predictions of experimentally measurable properties remains fundamentally limited by the need to approximate the unknown exchange-correlation (XC) functional. The traditional paradigm for improving accuracy has relied on increasingly elaborate hand-crafted functional forms. This approach has led to a longstanding trade-off between computational efficiency and accuracy, which remains insufficient for reliable predictive modelling of laboratory experiments. Here we introduce Skala, a deep learning-based XC functional that surpasses state-of-the-art hybrid functionals in accuracy across the main-group chemistry benchmark set GMTKN55 with an error of 2.8 kcal/mol, while retaining the lower computational cost characteristic of semi-local DFT. This demonstrated departure from the historical trade-off between accuracy and efficiency is enabled by learning non-local representations of electronic structure directly from data, bypassing the need for increasingly costly hand-engineered features. Leveraging an unprecedented volume of high-accuracy reference data from wavefunction-based methods, we establish that modern deep learning enables systematically improvable neural exchange-correlation models as training datasets expand, positioning first-principles simulations to become progressively more predictive.