Machine learning surrogate models for prediction of point defect vibrational entropy

The temperature variation of the defect densities in a crystal depends on vibrational entropy. This contribution to the system thermodynamics remains computationally challenging as it requires a diagonalization of the system's Hessian which scales as O(N-3) for a crystal made of N atoms. Here, to circumvent such a heavy computational task and make it feasible even for systems containing millions of atoms, the harmonic vibrational entropy of point defects is estimated directly from the relaxed atomic positions through a linear-in-descriptor machine learning approach of order O(N). With a size-independent descriptor dimension and fixed model parameters, an excellent predictive power is demonstrated on a wide range of defect configurations, supercell sizes, and external deformations well outside the training database. In particular, formation entropies in a range of 250k(B) are predicted with less than 1.6k(B) error from a training database whose formation entropies span only 25k(B) (training error less than 1.0k(B)). This exceptional transferability is found to hold even when the training is limited to a low-energy superbasin in the phase space while the tests are performed for a different liquid-like superbasin at higher energies.