Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models

TL;DR

This paper introduces a projection-based coarse-graining method for Langevin dynamics that preserves thermodynamic and kinetic properties, utilizing gEDMD and thermodynamic interpolation for efficient multi-state modeling.

Contribution

It develops a formalism combining projection methods, gEDMD, and thermodynamic interpolation to accurately model thermodynamics and kinetics in coarse-grained Langevin systems.

Findings

Accurately captures thermodynamic properties of the full model.

Effectively models kinetic transition timescales.

Extends across thermodynamic states without repeated simulations.

Abstract

Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general underdamped Langevin dynamics. Following the Zwanzig projection approach, we derive a closed-form expression for the coarse grained dynamics. In addition, we show how the generator Extended Dynamic Mode Decomposition (gEDMD) method, which was developed in the context of Koopman operator methods, can be used to model the CG dynamics and evaluate its kinetic properties, such as transition timescales. Finally, we combine our approach with thermodynamic interpolation (TI), a generative approach to transform samples between thermodynamic conditions, to extend the scope of the approach across thermodynamic states without repeated numerical simulations. Using a two-dimensional model system, we demonstrate that the proposed method allows to accurately capture the thermodynamic and kinetic properties of the full-space model.