Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functional

• URL: http://arxiv.org/abs/2306.17587v1
• Date: Fri, 30 Jun 2023 12:07:26 GMT
• Title: Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functional
• Authors: P. del Mazo-Sevillano and J. Hermann
• Abstract summary: We propose a new and efficient regularization method to train density functionals based on deep neural networks. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods. For the atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange--correlation functional.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange--correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For the atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange--correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.

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