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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.
This article was published in the following journal.
Name: The Journal of chemical physics
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A MACHINE LEARNING paradigm used to make predictions about future instances based on a given set of unlabeled paired input-output training (sample) data.
A MACHINE LEARNING paradigm used to make predictions about future instances based on a given set of labeled paired input-output training (sample) data.
SUPERVISED MACHINE LEARNING algorithm which learns to assign labels to objects from a set of training examples. Examples are learning to recognize fraudulent credit card activity by examining hundreds or thousands of fraudulent and non-fraudulent credit card activity, or learning to make disease diagnosis or prognosis based on automatic classification of microarray gene expression profiles drawn from hundreds or thousands of samples.
A type of ARTIFICIAL INTELLIGENCE that enable COMPUTERS to independently initiate and execute LEARNING when exposed to new data.
Process in which individuals take the initiative, in diagnosing their learning needs, formulating learning goals, identifying resources for learning, choosing and implementing learning strategies and evaluating learning outcomes (Knowles, 1975)