  Computing vibrational free energies ($F_{vib}$) and entropies ($S_{vib}$) has
posed a long standing challenge to the high-throughput ab initio investigation
of finite temperature properties of solids. Here we use machine-learning
techniques to efficiently predict $F_{vib}$ and $S_{vib}$ of crystalline
compounds in the Inorganic Crystal Structure Database. By employing descriptors
based simply on the chemical formula and using a training set of only 300
compounds, mean absolute errors of less than 0.04 meV/K/atom (15 meV/atom) are
achieved for $S_{vib}$ ($F_{vib}$), whose values are distributed within a range
of 0.9 meV/K/atom (300 meV/atom.) In addition, for training sets containing
fewer than 2,000 compounds the chemical formula alone is shown to perform as
well as, if not better than, four other more complex descriptors previously
used in the literature. The accuracy and simplicity of the approach mean that
it can be advantageously used for the fast screening of phase diagrams or
chemical reactions at finite temperatures.
