# Surrogate Functionals for Machine-Learned Orbital-Free Density Functional Theory

arXiv: https://arxiv.org/abs/2604.20458 · HTML: https://mlsanity.com/paper/2604.20458/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 33 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning](https://mlsanity.com/paper/2309.16578/) (2023)
- [Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materials](https://mlsanity.com/paper/2312.05388/) (2023)
- [Orbital-free Bond Breaking via Machine Learning](https://mlsanity.com/paper/1306.1812/) (2013)
- [KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory](https://mlsanity.com/paper/2305.13316/) (2023)

## Built on by (most cited first, 2 of 2)

- [Electron-Density-Informed Molecular Property Prediction Using Surrogate Functionals](https://mlsanity.com/paper/2610.13649/) (2026)
- [All-electron machine-learned orbital-free density functional for periodic CHNO systems](https://mlsanity.com/paper/2610.17975/) (2026)

## Abstract (arXiv)

We introduce surrogate functionals: machine-learned energy functionals for orbital-free density functional theory (OF-DFT) which are defined not by universal fidelity to a physical reference, but merely by the requirement that density optimization with a fixed procedure yields the true ground-state density. Helpfully, training surrogate functionals requires only ground-state densities, no energies or gradients away from the ground state. We here propose a gradient-descent-improvement loss that guarantees exponential convergence of the density to the ground state, and combine it with an adaptive sampling scheme that concentrates learning around the optimization trajectories actually visited during inference. On the QM9 and QMugs benchmarks, surrogate functionals achieve density errors competitive with or improving upon the state of the art for fully supervised machine-learned OF-DFT, while eliminating the need for the O(N3) orthononormalization step required by prior work, yielding improved runtime scaling for larger systems.