Kinetically Consistent Coarse Graining Using Kernel-Based Extended Dynamic Mode Decomposition

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Data-Driven Modeling

Background:

• Coarse-graining (CG) methods simplify complex molecular systems.
• Identifying accurate CG dynamics, especially slow timescales, remains challenging.
• Kernel-based Koopman analysis offers a data-driven approach to dynamics.

Purpose of the Study:

• To develop a method for inferring effective coarse-grained dynamics using kernel-based Koopman generators.
• To introduce a learning approach for effective diffusion in coarse-grained space.
• To evaluate the kinetic accuracy of CG models and infer complete effective dynamics.

Main Methods:

• Kernel-based Koopman analysis via the gEDMD method.
• A novel learning method for effective diffusion, akin to force matching.
• Integration with effective free energy models (e.g., force matching).
• Validation using a 2D model, alanine dipeptide, and Chignolin molecular dynamics data.

Main Results:

• The gEDMD method successfully identifies CG dynamics capturing slow transition timescales.
• The proposed learning method effectively models diffusion in the coarse-grained space.
• Accurate recovery of essential kinetic and thermodynamic properties of the full model was demonstrated.
• The method robustly reproduces system dynamics across different molecular models.

Conclusions:

• Kernel-based Koopman models provide a robust framework for accurate coarse-grained dynamics.
• The developed method allows for the inference of complete effective dynamics, including diffusion and free energy.
• Standard model validation techniques are sufficient for parameter determination.