Local and global perspectives on diffusion maps in the analysis of molecular systems

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Data Science

Background:

• Diffusion maps are powerful tools for analyzing high-dimensional data, particularly in molecular dynamics simulations.
• Identifying slow dynamics and sampling complex energy landscapes remain significant challenges in molecular modeling.

Purpose of the Study:

• To explore local and global perspectives of diffusion maps for analyzing molecular systems.
• To develop an enhanced sampling algorithm for accelerating molecular simulations.
• To approximate committor functions and identify metastable sets in molecular dynamics.

Main Methods:

• Utilizing diffusion maps to approximate the generator of Langevin dynamics.
• Applying diffusion maps to identify metastable sets and committor functions.
• Formalizing local equilibrium using quasi-stationary distributions.
• Developing and demonstrating an enhanced sampling algorithm.

Main Results:

• Diffusion maps effectively identify principal modes of molecular systems.
• The combination of diffusion maps with biasing accelerates sampling of the Boltzmann-Gibbs distribution.
• The proposed enhanced sampling algorithm shows practical relevance in simple models and molecular dynamics.

Conclusions:

• Diffusion maps provide a robust framework for understanding molecular dynamics, offering both global and local insights.
• The developed enhanced sampling method improves the efficiency of molecular simulations.
• This approach facilitates the study of complex molecular systems and their transitions.