Dimensional reduction of Markov state models from renormalization group theory

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Theoretical Physics

Background:

• Renormalization Group (RG) theory offers a framework for constructing rigorous effective theories from microscopic models.
• Markov state models (MSMs) are established as effective theories for Molecular Dynamics (MD) simulations.
• Systematic coarse-graining is crucial for reducing the complexity of molecular dynamics simulations.

Purpose of the Study:

• To develop a novel algorithm for clustering microstates into macrostates using real-space RG.
• To construct optimal, low-dimensional Markovian models for representing system relaxation kinetics.
• To validate the RG-based coarse-graining approach on diverse test systems.

Main Methods:

• Application of real-space Renormalization Group (RG) theory to stochastic models.
• Development of an algorithm for adaptive microstate clustering into macrostates.
• Validation using synthetic models and all-atom Molecular Dynamics (MD) simulations.

Main Results:

• The RG approach yields a systematic method for coarse-graining molecular dynamics data.
• The resulting low-dimensional models accurately represent the system's relaxation kinetics.
• The computational cost is manageable, even for large systems, enabling desktop analysis.

Conclusions:

• Markov state models derived via RG theory provide optimal coarse-grained representations.
• This method offers a computationally efficient pathway to understand complex molecular dynamics.
• The RG-based coarse-graining is a powerful tool for analyzing system dynamics.