An Iterative and Automatic Collective Variable Optimization Scheme via Unsupervised Feature Selection with CUR Matrix Decomposition

Phase transitions frequently involve surmounting significant energy barriers, necessitating the construction of collective variables (CVs) to facilitate enhanced sampling of high-energy structures in molecular dynamics simulations. However, optimizing CVs remains a formidable challenge, particularly when limited prior knowledge about the transition process is available. This study presents an unsupervised approach for CV optimization, which iteratively employs CUR matrix decomposition for feature selection and principal component analysis (PCA) for CV generation. The approach is validated using a hypothetical three-phase model of ultra-high-pressure hydrogen derived at the density functional theory level of theory to characterize transition pathways. CVs are constructed using feature variables extracted from simulated X-ray diffraction intensity spectra. Our fully unsupervised approach demonstrated self-correction capabilities in discovering probable phase-transition pathways. By relying solely on unbiased molecular dynamics simulations of meta-stable structures to construct the initial dataset, the free energy profile can be properly reproduced for the phase transitions among them, this suggests the potential for developing a highly autonomous approach to exploring complex systems with elusive physical mechanisms.