Finding Efficient Collective Variables: The Case of Crystallization

TL;DR

This paper compares two methods for identifying effective collective variables in enhanced sampling, finding that linear discriminant analysis is simpler and nearly as effective as the variational approach in crystallization studies.

Contribution

The study evaluates and compares linear discriminant analysis and variational conformational dynamics methods for selecting collective variables in crystallization simulations.

Findings

Both methods perform similarly in identifying collective variables.

Linear discriminant analysis is simpler and less computationally intensive.

Effective collective variables can be expressed as linear combinations of diffraction peak intensities.

Abstract

Several enhanced sampling methods such as umbrella sampling or metadynamics rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient collective variables. One is based on linear discriminant analysis, the other on a variational approach to conformational dynamics, and uses time-lagged independent component analysis. In this paper, we compare the performance of these two approaches in the study of the homogeneous crystallization of two simple metals. We focus on Na and Al and search for the most efficient collective variables that can be expressed as a linear combination of X-ray diffraction peak intensities. We find that the performances of the two methods are very similar. However, the method based on linear discriminant analysis, in its harmonic version, is to be preferred because it is simpler and much less computationally demanding.