## Details

Original language | English |
---|---|

Article number | 015011 |

Number of pages | 13 |

Journal | Machine Learning: Science and Technology |

Volume | 3 |

Issue number | 1 |

Publication status | Published - 15 Dec 2021 |

Externally published | Yes |

## 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

- Computer Science(all)
**Artificial Intelligence**- Computer Science(all)
**Human-Computer Interaction**- Computer Science(all)
**Software**

## Cite this

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- Harvard
- Apa
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- BibTeX
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**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

*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

*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

}

TY - JOUR

T1 - Machine learning the derivative discontinuity of density-functional theory

AU - Gedeon, Johannes

AU - Schmidt, Jonathan

AU - Hodgson, Matthew J.P.

AU - Wetherell, Jack

AU - Benavides-Riveros, Carlos L.

AU - Marques, Miguel A.L.

N1 - Funding Information: C L B-R acknowledges funding from “BiGmax”, the Max Planck Society’s research network on big-data-driven materials science.

PY - 2021/12/15

Y1 - 2021/12/15

N2 - 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.

AB - 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.

KW - Density functional theory

KW - Electronic structure

KW - Ensemble density functional theory

KW - Machine learning

KW - Quantum physics

UR - http://www.scopus.com/inward/record.url?scp=85123677837&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2106.16075

DO - 10.48550/arXiv.2106.16075

M3 - Article

AN - SCOPUS:85123677837

VL - 3

JO - Machine Learning: Science and Technology

JF - Machine Learning: Science and Technology

IS - 1

M1 - 015011

ER -