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 optimizing the CVs by iteratively applying the principal component analysis algorithm on the representative feature variables generated with the CUR method (an efficient feature space contraction algorithm that can be employed to seek the representative feature variables). 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 metastable structures to construct the initial dataset, the free energy profile can be properly reproduced for the phase transitions among them, which suggests the potential for developing a highly autonomous approach to exploring complex systems with elusive physical mechanisms.