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Machine learning modeling of Wigner intracule functionals for two electrons in one-dimension.

08:00 EDT 14th April 2019 | BioPortfolio

Summary of "Machine learning modeling of Wigner intracule functionals for two electrons in one-dimension."

In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function (W), thanks to a universal functional transformation (F), whose formal existence is akin to that of the exchange-correlation functional in density functional theory. While the exact dependence of F on W is unknown, a few approximate parametric models have been proposed in the past. Here, for a dataset of 923 one-dimensional external potentials with two interacting electrons, we apply machine learning to model F within the kernel Ansatz. We deal with over-fitting of the kernel to a specific region of phase-space by a one-step regularization not depending on any hyperparameters. Reference correlation energies have been computed by performing exact and Hartree-Fock calculations using discrete variable representation. The resulting models require W calculated at the Hartree-Fock level as input while yielding monotonous decay in the predicted correlation energies of new molecules reaching sub-chemical accuracy with training.

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This article was published in the following journal.

Name: The Journal of chemical physics
ISSN: 1089-7690
Pages: 144114

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