Anharmonic Phonons with Gaussian Processes

We provide a method for calculating anharmonic lattice dynamics (http://arxiv.org/abs/2405.05113), by building a surrogate machine-learning model based on Gaussian Processes (GPs). Due to the underlying Gaussian form of a GP, the model is infinitely differentiable. This allows us to train the model trained directly on forces (the derivative of PESs) reducing the evaluations required for a given accuracy. We can extend this differentiation to directly calculate second and third order force-constants using automatic differentiation (AD). For the five model materials we study, we find that the force-constants are in close agreement with a standard finite-displacement approach. We also compare our results with the recent cluster expansion technique implemented in HiPhive.py which requires a larger supercell to achieve the same level of accuracy. Our method appears to be linear scaling in the number of atoms at predicting both second and third-order (anharmonic) force-constants.