Practically, a set of MD simulations are performed at temperatures varying from T 0 to T 1 , from which the average internal energy U (T ) is extracted and the integral in Eq. 17 is numerically evaluated. Other TI expressions are also available to obtain the free energy shifts on changing volume or on arbitrary crystal deformations . TI based approaches have been applied to calculate relative phase stabilities in systems ranging from simple elemental metals to complex molecular crystals or highentropy alloys . Other applications include defect formation free energies and melting points . If the integration is coupled with ab initio molecular dynamics, the computational cost is large. Thus, there is great promise in reducing the burden with modern machine-learned force fields to obtain accurate free energies for more complex crystals.