Advances at the Intersection of Density Functional Theory and Artificial Intelligence

Density functional theory (DFT) has become one of the most successful computational methods for studying electronic structure, with broad applications in condensed matter physics, atomic and molecular physics, materials science, and chemistry. Extending the concept of DFT from electron density to particle density, classical density functional theory (cDFT) has likewise achieved success in soft matter and biophysics. As machine learning and artificial intelligence increasingly influence all areas of science and technology, they are poised to shape the future trajectory of DFT and cDFT development. This Collection, curated by the editors of the Physical Review family of journals, offers an early glimpse into how these emerging tools can further unlock the potential of a proven and highly successful computational method.

We have developed this collection in collaboration with the Division of Chemical Physics of the American Physical Society. We invite the readers to attend the associated Focus Session “Density Functional Theory at the Intersection of Traditional Electronic Structure Theory and AI/ML” at the APS Global Physics Summit 2026 in Denver.

This retrospective Collection brings together influential research previously published across the portfolio. These papers, selected by our editors for their contribution to the field, have all undergone our standard peer-review process.

DFT Development with Neural Networks

Combining DFT with the fundamental concepts of neural networks is an ambitious task. The following papers aim to establish a framework that unites the two fields, by embedding neural network concepts directly into the density functionals themselves. They have the potential to fundamentally reshape the future trajectory of DFT development.

Deep-Learning Density Functional Perturbation Theory
He Li, Zechen Tang, Jingheng Fu, Wen-Han Dong, Nianlong Zou, Xiaoxun Gong, Wenhui Duan, and Yong Xu
Phys. Rev. Lett. 132, 096401 (2024)

Neural-network Density Functional Theory Based on Variational Energy Minimization
Yang Li, Zechen Tang, Zezhou Chen, Minghui Sun, Boheng Zhao, He Li, Honggeng Tao, Zilong Yuan, Wenhui Duan, and Yong Xu
Phys. Rev. Lett. 133, 076401 (2024)

Neural network distillation of orbital dependent density functional theory
Matija Medvidović, Jaylyn C. Umana, Iman Ahmadabadi, Domenico Di Sante, Johannes Flick, and Angel Rubio
Phys. Rev. Research 7, 023113 (2025)

cDFT Development with Neural Networks

Similarly, incorporating neural networks directly into cDFT expands its capabilities into more complex systems and unlocks new discoveries. Using a trained network as a replacement for the free-energy functional, the following papers demonstrate the power of the combined approach by studying liquid-gas phase transitions in more realistic models.

Neural Density Functional Theory of Liquid-Gas Phase Coexistence
Florian Sammüller, Matthias Schmidt, and Robert Evans
Phys. Rev. X 15, 011013 (2025)

Hyperdensity Functional Theory of Soft Matter
Florian Sammüller, Silas Robitschko, Sophie Hermann, and Matthias Schmidt
Phys. Rev. Lett. 133, 098201 (2024)

Machine Learning with Data from Traditional DFT Calculations

Although efforts to fundamentally reshape the development of DFT have only just begun, we are already witnessing impact on scientific discovery, through the use of machine learning to process and distill the vast data generated by traditional DFT calculations. This straightforward approach has been applied across many fields, including condensed matter physics, atomic and molecular physics, materials science, and chemistry.

Carbon Capture Phenomena in Metal-Organic Frameworks with Neural Network Potentials
Yusuf Shaidu, Alex Smith, Eric Taw, and Jeffrey B. Neaton
PRX Energy 2, 023005 (2023)

Neural networks for the prediction of electronic excitation dynamics
Ethan P. Shapera and Cheng-Wei Lee
Phys. Rev. A 111, 012806 (2025)

Generative diffusion model for surface structure discovery
Nikolaj Rønne, Alán Aspuru-Guzik, and Bjørk Hammer
Phys. Rev. B 110, 235427 (2024)

Liquid-liquid phase transition of hydrogen and its critical point: Analysis from ab initio simulation and a machine-learned potential
Mathieu Istas, Scott Jensen, Yubo Yang, Markus Holzmann, Carlo Pierleoni, and David M. Ceperley
Phys. Rev. E 111, 045307 (2025)

High-throughput hybrid-functional DFT calculations of bandgaps and formation energies and multifidelity learning with uncertainty quantification
Mohan Liu, Abhijith Gopakumar, Vinay Ishwar Hegde, Jiangang He, and Chris Wolverton
Phys. Rev. Materials 8, 043803 (2024)

Accurate machine-learning predictions of coercivity in high-performance permanent magnets
Churna Bhandari, Gavin N. Nop, Jonathan D.H. Smith, and Durga Paudyal
Phys. Rev. Applied 22, 024046 (2024)

APS Journals

Advances at the Intersection of Density Functional Theory and Artificial Intelligence

DFT Development with Neural Networks

cDFT Development with Neural Networks

Machine Learning with Data from Traditional DFT Calculations

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