Kinetic energy density using machine learning for orbital-free density functional calculations

Inspired by the remarkable ongoing progress of the data-driven science approach, a predictive model is prepared to develop accurate one-dimensional kinetic energy density functionals (KEDF) using Machine Learning (ML). Starting from possible analytical forms of kinetic energy density [1,2] and by utilizing a variety of solvable models, an 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 by several orders of magnitudes. As more different potentials of model problems are mixed, the coefficients of the linear model significantly approach the analytic values of Thomas-Fermi (TF) and von Weizsäcker (vW), 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 (OFDFT) calculations.

[1] F. H. Alharbi and S. Kais, Int. J. Quantum Chem. 117, 25373 (2017).
[2] T. Gal and A. Nagy, J. Mol. Struct. 501-502, 167 (2000).