# Machine learning surrogate models for prediction of point defect vibrational entropy

Abstract : 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 diagonalisation of the system's Hessian which scales as $O(N^3)$ for a crystal made of N atoms. Here, to circumvent such an 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 of the training database. In particular, formation entropies in a range of 250 $k_{B}$ are predicted with less than 1.6 $k_B$ error from a training database whose formation entropies span only 25 $k_B$ (train error less than 1.0 kB. 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.
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https://hal-cea.archives-ouvertes.fr/cea-03775685
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Submitted on : Monday, September 12, 2022 - 10:30:38 PM
Last modification on : Wednesday, September 28, 2022 - 10:09:29 AM

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PhysRevMaterials.4.063802.pdf
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• HAL Id : cea-03775685, version 1

### Citation

Clovis Lapointe, Thomas D. Swinburne, Louis Thiry, Stéphane Mallat, Laurent Proville, et al.. Machine learning surrogate models for prediction of point defect vibrational entropy. Physical Review Materials, American Physical Society, 2020, 4 (6), pp.063802. ⟨cea-03775685⟩

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