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Understanding ionic behaviour under external electric fields is crucial todevelop electronic and energy-related devices using ion transport. In thisstudy, we propose a neural network (NN) model to predict the Born effectivecharges of ions along an axis parallel to an applied electric field from atomicstructures. The proposed NN model is applied to Li$_3$PO$_4$ as a prototype.The prediction error of the constructed NN model is 0.0376 $e$/atom. Incombination with an NN interatomic potential, molecular dynamics (MD)simulations are performed under a uniform electric field of 0.1 V/angstrom,whereby an enhanced mean square displacement of Li along the electric field isobtained, which seems physically reasonable. In addition, the external forcesalong the direction perpendicular to the electric field, originating from theoff-diagonal terms of the Born effective charges, are found to have anonnegligible effect on Li migration. Finally, additional MD simulations areperformed to examine the Li motion in an amorphous structure. The resultsreveal that Li migration occurs in various areas despite the absence ofexplicitly introduced defects, which may be attributed to the susceptibility ofthe Li ions in the local minima to the electric field. We expect that theproposed NN method can be applied to any ionic material, thereby leading toatomic-scale elucidation of ion behaviour under electric fields.

Prediction of Born effective charges using neural network to study ion  migration under electric fields: applications to crystalline and amorphous  Li$_3$PO$_4$