Generalized Langevin dynamics: Construction and numerical integration of non-Markovian particle-based models

TL;DR

This paper introduces a generalized Langevin dynamics (GLD) method for constructing and efficiently simulating non-Markovian coarse-grained models from detailed reference data, enabling accurate and scalable soft matter system studies.

Contribution

The paper develops a novel GLD approach with a linear-scaling algorithm for non-Markovian particle models, including a method for reconstructing memory kernels from fine-grained simulations.

Findings

GLD accurately reproduces fine-grained dynamics.

Achieves a simulation speedup of about 10,000 times.

Model transferability to different densities is demonstrated.

Abstract

We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a discretized generalized Langevin equation with distance-dependent two-particle contributions to the self- and pair-memory kernels. The memory kernels are iteratively reconstructed from the dynamical correlation functions of an underlying fine-grained system. We develop a simulation algorithm for this class of non-Markovian models that scales linearly with the number of coarse-grained particles. Our GLD method is suitable for coarse-grained studies of systems with incomplete time scale separation, as is often encountered, e.g., in soft matter systems. We apply the method to a suspension of nanocolloids with frequency-dependent hydrodynamic interactions. We show that the results from GLD simulations perfectly reproduce the dynamics of the underlying fine-grained system. The effective speedup of these simulations amounts to a factor of about $10^4$. Additionally, the transferability of the coarse-grained model with respect to changes of the nanocolloid density is investigated. The results indicate that the model is transferable to systems with nanocolloid densities that differ by up to one order of magnitude from the density of the reference system.