  We study the dependence of kinetic energy densities (KED) on
density-dependent variables that have been suggested in previous works on
kinetic energy functionals (KEF) for orbital-free DFT (OF-DFT). We focus on the
role of data distribution and on data and regressor selection. We compare
unweighted and weighted linear and Gaussian process regressions of KED for
light metals and a semiconductor. We find that good quality linear regression
resulting in good energy-volume dependence is possible over density-dependent
variables suggested in previous literature. This is achieved with weighted
fitting based on KED histogram. With Gaussian process regressions, excellent
KED fit quality well exceeding that of linear regressions is obtained as well
as a good energy-volume dependence which was somewhat better than that of best
linear regressions. We find that while the use of the effective potential as a
descriptor improves linear KED fitting, it does not improve the quality of the
energy-volume dependence with linear regressions but substantially improves it
with Gaussian process regression. Gaussian process regression is also able to
perform well without data weighting.
