Modeling coarse-grained lattice dynamics with ab initio generalized Langevin equation*

We model the dynamics of coarse-grained variables defined on Bravais lattice with multi-dimensional ab initio generalized Langevin equation (AIGLE). The memory kernel and the noise generator in AIGLE are learned from molecular dynamics (MD) data and constrained by the fluctuation-dissipation theorem.

 

We demonstrate the approach with a study of the ferroelectric crystal lead titanate. We introduce a local kernel approximation and train an infinite-dimensional AIGLE to model the dynamics of interacting local dipole moments on a coarse-grained lattice. AIGLE is shown to be consistent with MD data not only for the autocorrelation of local dipole moments and global polarization, but also for the cross-correlation between neighboring local dipoles.