Inspired by the recent successes in training force fields on geometry relaxations, we here propose to build an MLFF trained on the relaxation trajectories already available when constructing a cluster expansion model. We then use this force field as a surrogate model for DFT to perform lattice dynamics calculations for the training structures to include vibrational free energies into the cluster expansion model with low additional computational cost. In this Letter, we demonstrate this method for two compositionally simple materials, the Na 1 -x K x Cl (rock salt structure) and Ag 1 -x Pd x (fcc structure) solid solutions as archetypical representatives for ionic and metallic solid solutions, respectively. For the former, previous simulations have shown that vibrational entropy is key to obtaining a miscibility gap in agreement with experimental results .