The most important indicator of performance in the present case is the ability to accurately predict the phonon frequencies, and even more importantly the vibrational free energies derived thereof. Fig. , S5 and S6 show comparisons of phonon dispersions, density of states (DOS) and vibrational free energies for a selected set of training structures, including the end-members (Fig. ). It is evident that the MLFF reproduces the DFT phonon dispersions and DOS with overall good agreement, and in the temperature range of interest, the error in vibrational free energy is typically on the order of 1-2 meV atom -1 . As DFT internal energies are commonly converged to around 1 meV atom -1 , this should be considered an acceptable error range. Note, however, that the errors are given per atom, whereas the relevant energies for the construction of CEs are per metal atom (or formula unit), i.e., twice as large.