Machine learning the derivative discontinuity of density-functional theory

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Johannes Gedeon
  • Jonathan Schmidt
  • Matthew J.P. Hodgson
  • Jack Wetherell
  • Carlos L. Benavides-Riveros
  • Miguel A.L. Marques

External Research Organisations

  • Martin Luther University Halle-Wittenberg
  • University of Durham
  • Université Paris-Saclay
  • Max Planck Institute for the Physics of Complex Systems
  • CNR Area della Ricerca di Roma 1 - Montelibretti (ARRM1)
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Details

Original languageEnglish
Article number015011
Number of pages13
JournalMachine Learning: Science and Technology
Volume3
Issue number1
Publication statusPublished - 15 Dec 2021
Externally publishedYes

Abstract

Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to these problems by training a neural network as the universal functional of density-functional theory that (a) depends explicitly on the number of particles with a piece-wise linearity between the integer numbers and (b) reproduces the derivative discontinuity of the exchange-correlation energy. This is achieved by using an ensemble formalism, a training set containing fractional densities, and an explicitly discontinuous formulation.

Keywords

    Density functional theory, Electronic structure, Ensemble density functional theory, Machine learning, Quantum physics

ASJC Scopus subject areas

Cite this

Machine learning the derivative discontinuity of density-functional theory. / Gedeon, Johannes; Schmidt, Jonathan; Hodgson, Matthew J.P. et al.
In: Machine Learning: Science and Technology, Vol. 3, No. 1, 015011, 15.12.2021.

Research output: Contribution to journal › Article › Research › peer review

Gedeon, J, Schmidt, J, Hodgson, MJP, Wetherell, J, Benavides-Riveros, CL & Marques, MAL 2021, 'Machine learning the derivative discontinuity of density-functional theory', Machine Learning: Science and Technology, vol. 3, no. 1, 015011. https://doi.org/10.48550/arXiv.2106.16075, https://doi.org/10.1088/2632-2153/ac3149
Gedeon, J., Schmidt, J., Hodgson, M. J. P., Wetherell, J., Benavides-Riveros, C. L., & Marques, M. A. L. (2021). Machine learning the derivative discontinuity of density-functional theory. Machine Learning: Science and Technology, 3(1), Article 015011. https://doi.org/10.48550/arXiv.2106.16075, https://doi.org/10.1088/2632-2153/ac3149
Gedeon J, Schmidt J, Hodgson MJP, Wetherell J, Benavides-Riveros CL, Marques MAL. Machine learning the derivative discontinuity of density-functional theory. Machine Learning: Science and Technology. 2021 Dec 15;3(1):015011. doi: 10.48550/arXiv.2106.16075, 10.1088/2632-2153/ac3149
Gedeon, Johannes ; Schmidt, Jonathan ; Hodgson, Matthew J.P. et al. / Machine learning the derivative discontinuity of density-functional theory. In: Machine Learning: Science and Technology. 2021 ; Vol. 3, No. 1.
Download
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AU - Wetherell, Jack

AU - Benavides-Riveros, Carlos L.

AU - Marques, Miguel A.L.

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