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

2025-12-03

AI Summary

To address the longstanding challenge of simultaneously preserving thermodynamic and kinetic properties in coarse-grained (CG) modeling, this work introduces a closed-form, underdamped Langevin CG framework grounded in the Zwanzig projection operator formalism. Methodologically, it innovatively integrates generative extended dynamic mode decomposition (gEDMD) with thermodynamic interpolation, enabling— for the first time—joint preservation of kinetics and free-energy landscapes across multiple thermodynamic states without requiring repeated simulations per state. The resulting CG model explicitly predicts conformational transition timescales. Validation on a two-dimensional multistable system demonstrates high-fidelity reproduction of both thermodynamics (free-energy surfaces) and kinetics (relaxation times, transition pathways) relative to all-atom reference data. This approach establishes a new paradigm for efficient, thermodynamically consistent, and dynamically accurate multiscale modeling of biomolecular conformational dynamics.

Technology Category

• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Develops a projection-based coarse-graining method for underdamped Langevin dynamics
• Uses gEDMD to model coarse-grained kinetics and transition timescales
• Combines with thermodynamic interpolation to extend across states without resimulation

Innovation

• Projection-based coarse-graining for underdamped Langevin dynamics
• Using gEDMD to model kinetics and transition timescales
• Combining with thermodynamic interpolation across states