Differentiable Gaussian Process Force Constants

Gaussian processes are one machine learning method to describe Potential Energy Surfaces (PESs). Gaussian processes are naturally Bayesian (probabilistic).

The reference data is often an electronic structure from which the Gaussian processes regression (GPR) model is conditioned (trained). Due to their Gaussian structure, we can directly differentiate the model. This allows the model to be trained directly on forces (the derivative of PESs), reducing the calculations required for a given accuracy of PES evaluation. This differentiation can be extended to compute the second and the third derivative of PESs, force constants (FCs), by using automatic differentiation (AD). By performing linear operations between arbitrary derivative orders of the GPR model, the covariance functions among PESs, forces and those FCs can be achieved. We implement this method within the Julia language, in the GPFC.jl package. We compare our technique of crystalline anharmonic property calculations with more standard approaches of finite difference and cluster expansion.