Highly accurate machine learning model for kinetic energy density functional

Abstract

Inspired by the remarkable ongoing progress of data-driven approaches, a very accurate predictive model is developed to estimate one-dimensional kinetic energy density functionals (KEDF) using Machine Learning (ML). Starting from possible analytical forms of kinetic energy density and by utilizing a variety of solvable models, a simple – yet highly – accurate linear regression model is statistically trained to estimate the kinetic energy as functionals of the density. The mean relative accuracy for even a small number of randomly generated potentials is found to be better than the standard KEDF (Thomas-Fermi (TF) and von Weizsäcker (vW)) by several orders of magnitudes. As more different potentials of model problems are mixed, the coefficients of the linear model significantly approach the known values of Thomas-Fermi and von Weizsäcker, suggesting the reliability of the statistical training approach. This work can provide an important step toward more accurate large-scale orbital free density functional theory (OF-DFT) calculations.