Ab initio Generalized Langevin Equation

Pinchen Xie, Roberto Car, Weinan E., submitted to Proc. Nat. Acad. Sci. 2023, arXiv preprint arXiv:2211.06558

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 opens the door to carrying out first-principles multi-scale modeling for a variety of systems. Here, we demonstrate this capability with a study of the dynamics of twin domain walls 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.