The static CEs are fitted against total energies of all 631 systems, and the temperature dependent CEs are fitted separately at each temperature by adding the vibrational free energy to each training structure. Systems with imaginary modes in their phonon dispersions are removed from the fitting, since the free energy is ill-defined in these cases . Phase diagrams for each system are simulated using Monte Carlo simulations in the variance-constrained semi-grand canonical (VCSGC) ensemble , which allows for accurate simulations across phase boundaries, as implemented in the MCHAMMER module of ICET .