In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function (), thanks to a universal functional transformation (), whose formal existence is akin to that of the exchange-correlation functional in density functional theory. While the exact dependence of on 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 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 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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