Analysis of Molecular Dynamics Simulation Data via Statistical Distances between Covariance Matrices

Area of Science:

• Computational chemistry
• Materials science
• Statistical mechanics

Background:

• Molecular dynamics (MD) simulations generate vast, high-dimensional data challenging traditional analysis.
• Existing dimensionality reduction and feature extraction methods face limitations in data efficiency and computational cost.
• Analyzing atomic behaviors to understand macroscopic material properties requires advanced analytical techniques.

Purpose of the Study:

• To develop a data-efficient statistical framework for analyzing MD simulation data.
• To extract meaningful features characterizing system dynamics using covariance matrices.
• To correlate extracted features with macroscopic physical properties and distinguish between material states.

Main Methods:

• Analysis of particle data distributions via covariance matrices (second-order moments).
• Quantification of system state discrepancies using statistical distances between covariance matrices.
• Application of dimensionality reduction to the distance matrix for feature extraction.

Main Results:

• A linear correlation was observed between the first principal component and the diffusion coefficient in Lennard-Jones systems.
• The method successfully distinguished between ice and liquid water phases.
• Global physical properties were effectively inferred from local statistical information (covariance matrices).

Conclusions:

• The proposed statistical framework offers a data-efficient alternative for analyzing complex molecular systems.
• Covariance matrix analysis combined with dimensionality reduction can characterize system dynamics and phase transitions.
• This approach facilitates the elucidation of macroscopic properties from microscopic atomic behaviors in MD simulations.