Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin...

Area of Science:

• Computational physics
• Soft matter physics
• Statistical mechanics

Background:

• Generalized Langevin equation (GLE) models particle motion with memory effects.
• Numerical simulation of GLEs requires solving stochastic delay-differential equations and estimating memory kernels.
• Accurate modeling of dissipative forces is crucial for understanding complex systems.

Purpose of the Study:

• To develop a data-driven approach for constructing Markov models from velocity autocorrelation functions.
• To bypass the explicit calculation of memory kernels in GLE simulations.
• To provide a robust method for dynamic coarse-graining in soft matter systems.

Main Methods:

• Utilized equidistant samples of the velocity autocorrelation function.
• Employed a variant of the Prony method for exponential interpolation.
• Applied the positive real lemma from model reduction theory.
• Represented the memory kernel using auxiliary variables.

Main Results:

• Successfully computed data-driven Markov models for particle motion.
• Accurately reproduced velocity autocorrelation functions and memory kernels.
• Demonstrated efficacy in cases of anomalous diffusion and molecular dynamics simulations.
• Showcased robustness against significant statistical noise.

Conclusions:

• The developed method offers an efficient alternative to traditional GLE simulations.
• It accurately captures system dynamics without explicit memory kernel estimation.
• The approach is valuable for coarse-grained simulations of complex soft matter systems.