Iterative Reconstruction of Memory Kernels

Abstract

In recent years it has become increasingly popular to construct coarse-grained models with nonMarkovian dynamics in order to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the extraction of the dynamical properties, namely the memory kernel, from equilibrium all-atom simulations. In this paper we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed non-iterative techniques, it ensures by construction that the target correlation functions of the original fine-grained systems are reproduced accurately by the coarse-grained system, regardless of time step and discretization effects. Furthermore, we also propose a new numerical integrator for generalized Langevin equations that is significantly more accurate then the more commonly used generalization of the Velocity-Verlet integrator.We demonstrate the performance of the above described methods using the example of backflow induced memory in the Brownian diffusion of a single colloid. For this system we are able to reconstruct realistic coarse-grained dynamics with time steps about 200 times larger than used in the original molecular dynamics simulations.

Functional Macromolecular Systems: Kinetic Pathways to Obtain Tailored Structures

“…Actually for liquid crystals it has recently been demonstrated that different modes of structural relaxation experience different time mappings compared to the atomistic counterpart, which is especially relevant for non‐equilibrium processes . More recently, projector–operator techniques have been devised to predict the dynamics of the coarse‐grained degrees of freedom on the basis of the underlying microscopic dynamics and, importantly, to tailor them by thermostats . An alternative Ansatz employs Markov state models to identify dynamical processes and adjust coarse‐grained models to arrive at a homogeneous time scaling …”

“…[58,59] More recently, projector-operator techniques have been devised to predict the dynamics of the coarsegrained degrees of freedom on the basis of the underlying microscopic dynamics and, importantly, to tailor them by thermostats. [60][61][62] An alternative Ansatz employs Markov state models to identify dynamical processes and adjust coarsegrained models to arrive at a homogeneous time scaling. [63][64][65] 2.…”

Molecular Dynamics Simulation of High Density DNA Arrays

“…If required, the transport properties in the CG and AT parts of the system can be matched. This can be accomplished using local thermostats [117,118] or via the Mori-Zwanzig projection formalism [119][120][121][122][123][124] incorporating memory effects in the generalized Langevin equation. CG potentials are also density and temperature dependent [55,[125][126][127].…”

Memory-induced motion reversal in Brownian liquids

“…Bao et al 29 investigated breaking of ergodicity due to memory in non-Markovian Brownian dynamics. Recently, iterative methods have been developed to reconstruct memory kernels for generalized Langevin equations from molecular dynamics simulations by matching the force autocorrelation function or the velocity autocorrelation function between both methods 30,31 .…”