  We propose a machine-learning-based (ML-based) method for efficiently
predicting atomic diffusivity in crystals, in which the potential energy
surface (PES) of a diffusion carrier is partially evaluated by first-principles
calculations. To preferentially evaluate the region of interest governing the
atomic diffusivity, a statistical PES model based on a Gaussian process
(GP-PES) is constructed and updated iteratively from known information on
already-computed potential energies (PEs). In the proposed method, all local
energy minima (stable & metastable sites) and elementary processes of atomic
diffusion (atomic jumps) are explored on the predictive mean of the GP-PES. The
uncertainty of jump frequency in each elementary process is then estimated on
the basis of the variance of the GP-PES. The acquisition function determining
the next grid point to be computed is designed to reflect the impacts of the
uncertainties of jump frequencies on the uncertainty of the macroscopic atomic
diffusivity. The numerical solution of the master equation is here employed to
readily estimate the atomic diffusivity, which enables us to design the
acquisition function reflecting the centrality of each elementary process.
