Machine learning the derivative discontinuity of density-functional theory

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

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

Externe Organisationen

  • Martin-Luther-Universität Halle-Wittenberg
  • University of Durham
  • Universität Paris-Saclay
  • Max-Planck-Institut für Physik komplexer Systeme
  • CNR Area della Ricerca di Roma 1 - Montelibretti (ARRM1)
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer015011
Seitenumfang13
FachzeitschriftMachine Learning: Science and Technology
Jahrgang3
Ausgabenummer1
PublikationsstatusVeröffentlicht - 15 Dez. 2021
Extern publiziertJa

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.

ASJC Scopus Sachgebiete

Zitieren

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, Jahrgang 3, Nr. 1, 015011, 15.12.2021.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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, Jg. 3, Nr. 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), Artikel 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 Dez 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 ; Jahrgang 3, Nr. 1.
Download
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AU - Gedeon, Johannes

AU - Schmidt, Jonathan

AU - Hodgson, Matthew J.P.

AU - Wetherell, Jack

AU - Benavides-Riveros, Carlos L.

AU - Marques, Miguel A.L.

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