  Accurate prediction of thermodynamic properties requires an extremely
accurate representation of the free energy surface. Requirements are twofold --
first, the inclusion of the relevant finite-temperature mechanisms, and second,
a dense volume-temperature grid on which the calculations are performed. A
systematic workflow for such calculations requires computational efficiency and
reliability, and has not been available within an ab initio framework so far.
Here, we elucidate such a framework involving direct upsampling, thermodynamic
integration and machine-learning potentials, allowing us to incorporate, in
particular, the full effect of anharmonic vibrations. The improved methodology
has a five-times speed-up compared to state-of-the-art methods. We calculate
equilibrium thermodynamic properties up to the melting point for bcc Nb,
magnetic fcc Ni, fcc Al and hcp Mg, and find remarkable agreement with
experimental data. Strong impact of anharmonicity is observed specifically for
Nb. The introduced procedure paves the way for the development of ab initio
thermodynamic databases.
