  Oxyhydrides have drawn attention because of their fast ion conductivity and
strong reducing properties. Recently, hydride ion migration in
SrTiO$_{3-x}$H$_{x}$ oxyhydride crystals has been investigated, showing that
hydride ion migration is blocked by slow oxygen diffusion. In this study, we
investigate the hydride-ion migration mechanism using a kinetic Monte Carlo
approach to understanding the relationship between the hydride and oxygen ions.
The difficulties in applying the method to hydride and oxygen ion migration
involve complex changes in the ionic migration barrier, which shifts
dynamically depending on the characteristics of the surrounding hydride and
oxygen ions. We can predict these complex changes using a machine-learning
neural network model. The simulation can then be performed using this model to
predict the temperature-dependent ionic-migration behavior. We found that our
simulation results with respect to the activation barrier for hydride ion
diffusion accorded well with those obtained by experiment. We also found that
hydride ion migration is affected by slow oxygen diffusion and that oxygen
diffusion is accelerated by changes in the ionic migration barriers. The
parallel-processing efficiency of our proposed method was 84.92 \% for our
1,000-CPU implementation, suggesting that the approach should be widely
applicable to simulations of ionic migration in crystals at a reasonable
computational cost.
