<i>k</i>-Means Clustering in Fingerprint-Based Configuration Selection for Fitting Interatomic Potentials

In this study, we present a method for selecting an arbitrary number of distinct configurations from a larger data set by applying <i>k</i>-means clustering to atomistic configuration fingerprints based on the CrystalNN model and radial distribution function (RDF). This approach improves the accuracy of fitting classical molecular dynamics interatomic potentials to density functional theory (DFT) data for both energies and forces while requiring fewer configurations than random selection. We demonstrate this improvement by fitting an embedded-atom method (EAM) potential for titanium, using various configurational sizes from an initial set of 1800 configurations. The <i>k</i>-means clustering consistently achieves better precision and lower standard deviations for a smaller number of configurations than random selection. The results also suggest that only about 30 configurations are sufficient to obtain an EAM model that describes well the full set of 1800 configurations in terms of energies and forces. Additionally, t-distributed stochastic neighbor embedding (t-SNE) method was used to reduce the configuration fingerprints into 2D space, and it revealed an overlap between two configuration subsets with and without Ti vacancy, indicating similar atomic environments. This similarity is captured by <i>k</i>-means clustering but not by random selection. Furthermore, when the overlapping configurations with vacancies were excluded from the <i>k</i>-means algorithm and used only as a test set, their energy and force predictions showed similar precision to those when they were included. This indicates that the overlapping configurations in the 2D t-SNE space indeed imply potential information redundancy among the atomistic configurations.