Dimensional Reduction of Markov State Models from Renormalization Group Theory

TL;DR

This paper introduces a method based on Renormalization Group theory to reduce the dimensionality of Markov State Models, enabling efficient and optimal coarse-grained representations of molecular dynamics systems.

Contribution

It develops a novel algorithm for clustering microstates into macrostates using Real Space RG, providing a systematic way to obtain low-dimensional, Markovian models of relaxation kinetics.

Findings

The method accurately captures system relaxation dynamics.

Computational cost remains manageable for large microstate sets.

Validated on synthetic and real all-atom MD systems.

Abstract

Renormalization Group (RG) theory provides the theoretical framework to define Effective Theories (ETs), i.e. systematic low-resolution approximations of arbitrary microscopic models. Markov State Models (MSMs) are shown to be rigorous ETs for Molecular Dynamics (MD). Based on this fact, we use Real Space RG to vary the resolution of a MSM and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.