Anharmonic phonons with Gaussian processes

TL;DR

This paper introduces a Gaussian process-based surrogate model for anharmonic lattice dynamics, enabling efficient and differentiable calculations of force-constants directly from forces, with results comparable to standard methods.

Contribution

The authors develop a Gaussian process model that directly trains on forces to compute anharmonic force-constants, offering a differentiable, scalable alternative to traditional finite-displacement approaches.

Findings

Force-constants closely match finite-displacement results

Method scales linearly with the number of atoms

Enables direct calculation of second and third order force-constants

Abstract

We provide a method for calculating anharmonic lattice dynamics, by building a surrogate 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. Our method appears to be linear scaling in the number of atoms at predicting both second and third-order (anharmonic) force-constants.