Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Machine learning and density functional theory

Over the past decade machine learning has made significant advances in approximating density functionals, but whether this signals the end of human-designed functionals remains to be seen. Ryan Pederson, Bhupalee Kalita and Kieron Burke discuss the rise of machine learning for functional design.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

References

  1. Douglas, M. R. Machine learning as a tool in theoretical science. Nat. Rev. Phys. 4, 145–146 (2022).

    Article  Google Scholar 

  2. Austin, B. et al. Nersc-10 Workload Analysis (Data from 2018) (NERSC, 2020); https://portal.nersc.gov/project/m888/nersc10/workload/N10_Workload_Analysis.latest.pdf.

  3. Cohen, A. J., Mori-Sánchez, P. & Yang, W. Challenges for density functional theory. Chem. Rev. 112, 289–320 (2012).

    Article  Google Scholar 

  4. Snyder, J. C. et al. Finding density functionals with machine learning. Phys. Rev. Lett. 108, 253002 (2012).

    ADS  Article  Google Scholar 

  5. Brockherde, F. et al. Bypassing the Kohn-Sham equations with machine learning. Nat. Commun. 8, 872 (2017).

    ADS  Article  Google Scholar 

  6. Nagai, R., Akashi, R. & Sugino, O. Completing density functional theory by machine learning hidden messages from molecules. npj Comput. Mater. 6, 43 (2020).

    ADS  Article  Google Scholar 

  7. Li, L. et al. Kohn-Sham equations as regularizer: Building prior knowledge into machine-learned physics. Phys. Rev. Lett. 126, 036401 (2021).

    ADS  Article  Google Scholar 

  8. Kirkpatrick, J. et al. Pushing the frontiers of density functionals by solving the fractional electron problem. Science 374, 1385–1389 (2021).

    ADS  Article  Google Scholar 

  9. Cruz, F. G., Lam, K.-C. & Burke, K. Exchange−correlation energy density from virial theorem. J. Phys. Chem. A 102, 4911 (1998).

    Article  Google Scholar 

  10. Perdew, J. P. Artificial intelligence “sees” split electrons. Science 374, 1322–1323 (2021).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

Work supported by DOE DE-SC0008696 (R.P.) and NSF CHE-2154371 (B.K., K.B.).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kieron Burke.

Ethics declarations

Competing interests

The authors declare no competing interests.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pederson, R., Kalita, B. & Burke, K. Machine learning and density functional theory. Nat Rev Phys 4, 357–358 (2022). https://doi.org/10.1038/s42254-022-00470-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s42254-022-00470-2

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing