A Systematic Analysis of the Memory term in Coarse-Grained models: the case of the Markovian Approximation

TL;DR

This paper analyzes the memory term in coarse-grained models using the Mori-Zwanzig formalism, proposing a data-driven approach to approximate memory and fluctuation terms within the Markovian framework.

Contribution

It introduces a rational basis for approximating memory and fluctuation terms in CG models using data-driven methods, simplifying their derivation.

Findings

Proposes a Markovian approximation for memory and fluctuation terms.

Provides a data-driven methodology for coarse-grained modeling.

Analyzes the relation between memory terms and Markovian assumptions.

Abstract

The systematic development of Coarse-Grained (CG) models via the Mori-Zwanzig projector operator formalism requires the explicit description of several terms, including a deterministic drift term, a dissipative memory term and a random fluctuation term. In many applications, the memory and fluctuation terms are related by the fluctuation-dissipation relation and are, in general, more challenging to derive than the drift term. In this work we analyse an approximation of the memory term and propose a rational basis for a data-driven approach to an approximation of the memory and fluctuating terms which can be considered included in the class of the Markovian ones.