  Orbital-free density functional theory (OFDFT) offers a challenging way of
electronic-structure calculations scaled as $\mathcal{O}(N)$ computation for
system size $N$. We here develop a scheme of the OFDFT calculations based on
the accurate and transferrable kinetic-energy density functional (KEDF) which
is created in an unprecedented way using appropriately constructed neural
network (NN). We show that our OFDFT scheme reproduces the electron density
obtained in the state-of-the-art DFT calculations and then provides accurate
structural properties of 24 different systems, ranging from atoms, molecules,
metals, semiconductors and an ionic material. The accuracy and the
transferability of our KEDF is achieved by our NN training system in which the
kinetic-energy functional derivative (KEFD) at each real-space grid point is
used. The choice of the KEFD as a set of training data is essentially
important, because first it appears directly in the Euler equation which one
should solve and second, its learning assists in reproducing the physical
quantity expressed as the first derivative of the total energy. More generally,
the present development of KEDF $T[\rho]$ is in the line of systematic
expansion in terms of the functional derivatives $\delta^{\ell_1} T/\delta
\rho^{\ell_1}$ through progressive increase of $\ell_1$. The present numerical
success demonstrates the validity of this approach. The computational cost of
the present OFDFT scheme indeed shows the $\mathcal{O}(N)$ scaling, as is
evidenced by the computations of the semiconductor SiC used in power
electronics.
