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

Molecular dynamics (MD) simulations are powerful tools for elucidating the macroscopic physical properties of materials from microscopic atomic behaviors. However, the massive, high-dimensional data sets generated by MD simulations pose a significant challenge for analysis, necessitating efficient dimensionality reduction and feature extraction techniques. While existing methods such as principal component analysis and unsupervised learning have been utilized, issues regarding data efficiency and computational cost remain. In this study, we propose a statistical analysis framework focusing on the analysis of the particle data distributions through their covariance matrices, corresponding to the second-order moments of MD trajectory data. Discrepancies between system states are quantified using statistical distances between these covariance matrices. By applying dimensionality reduction to the resulting distance matrix, we extract lower-dimensional features that characterize the systems' dynamics. We validate the proposed method using Lennard-Jones (LJ) particle systems under different temperature conditions, as well as separate bulk systems of ice and liquid water. The results of LJ particles demonstrate an approximately linear correlation between the first principal component obtained through dimensionality reduction of the distance matrix and the diffusion coefficient. This suggests that global physical properties can be effectively inferred from local statistical information, such as covariance matrices, offering a data-efficient alternative for analyzing complex molecular systems. Furthermore, in the case of separate bulk systems of ice and liquid water, the method successfully distinguishes between the two phases, highlighting its potential for characterizing phase transitions and structural differences in molecular systems.