Ab Initio Generalized Langevin Equations

We propose an approach for learning accurately the dynamics of slow collective variables from atomistic data obtained from ab-initio quantum mechanical theory, using generalized Langevin equations (GLE). The force fields, memory kernel, and noise generator are constructed within the Mori-Zwanzig formalism under the constraint imposed by the fluctuation-dissipation theorem. Combined with Deep Potential Molecular Dynamics (DeePMD) and density functional theory, this GLE approach allows us to carry out first-principles multi-scale modeling for a variety of systems. We demonstrate this capability with a study of the dynamics of a simple domain wall in ferroelectric lead titanate. The importance of memory effects is illustrated by the fact that while ab-initio GLE agrees well with molecular dynamics at near-equilibrium conditions, Markovian Langevin dynamics underestimates the rate of rare events by several orders of magnitude.