  An axiomatic approach is herein used to determine the physically acceptable
forms for general $D$-dimensional kinetic energy density functionals (KEDF).
The resulted expansion captures most of the known forms of one-point KEDFs. By
statistically training the KEDF forms on a model problem of non-interacting
kinetic energy in 1D (6 terms only), the mean relative accuracy for 1000
randomly generated potentials is found to be better than the standard KEDF by
several orders of magnitudes. The accuracy improves with the number of occupied
states and was found to be better than $10^{-4}$ for a system with four
occupied states. Furthermore, we show that free fitting of the coefficients
associated with known KEDFs approaches the exactly analytic values. The
presented approach can open a new route to search for physically acceptable
kinetic energy density functionals and provide an essential step towards more
accurate large-scale orbital free density functional theory calculations.
