Iterative Reconstruction of Memory Kernels

TL;DR

This paper introduces an iterative method for accurately reconstructing memory kernels in non-Markovian coarse-grained models, enabling larger simulation time steps and improved numerical integration for systems like colloidal diffusion.

Contribution

It presents a novel iterative approach for memory kernel reconstruction that guarantees accurate correlation function reproduction and introduces a more precise integrator for generalized Langevin equations.

Findings

Successfully reconstructed realistic coarse-grained dynamics with 200x larger time steps.

Ensured target correlation functions are accurately reproduced regardless of discretization.

Demonstrated improved numerical accuracy over traditional integrators.

Abstract

In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics 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 article, we propose an iterative method for memory reconstruction from dynamical correlation functions. Compared to previously proposed noniterative 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 than 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 those used in the original molecular dynamics simulations.