# Accelerating Finite-temperature Kohn-Sham Density Functional Theory with Deep Neural Networks

arXiv: https://arxiv.org/abs/2010.04905 · HTML: https://mlsanity.com/paper/2010.04905/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Scientific Machine Learning for Modeling and Simulating Complex Fluids](https://mlsanity.com/paper/2210.04431/) (2022)
- [D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory](https://mlsanity.com/paper/2303.00399/) (2023)
- [Towards A Transferable Acceleration Method for Density Functional Theory](https://mlsanity.com/paper/2509.25724/) (2025)
- [Learning Partial Differential Equations by Spectral Approximates of General Sobolev Spaces](https://mlsanity.com/paper/2301.04887/) (2023)
- [Grad DFT: a software library for machine learning enhanced density functional theory](https://mlsanity.com/paper/2309.15127/) (2023)
- [Machine Learning Time Propagators for Time-Dependent Density Functional Theory Simulations](https://mlsanity.com/paper/2508.16554/) (2025)

## Abstract (arXiv)

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.