where r kk ′ ,i and r kk ′ ,j are the bond distance between k-th and k ′ -th atoms of configuration i and configuration j, respectively. N bond = (N bond + 1)N bond /2 is the number of atomic bonds. All permutation equivalent points are considered in the similarity calculations. The second criterion requires us to sort the points via their uncertainty. If there are too many points left after the selection of the first criterion, we only save N MS points that have the largest uncertainty ("MS" stands for max-sample). Besides, the points whose uncertainty is less than the given cut-off value U cut would still be removed. If the maximum uncertainty in the new set is larger than the stop threshold U stop (doesn't have to be equal to U cut ), the points in the new set will be added to the new training set, and a new sampling cycle will begin. Otherwise, the sampling would stop since the uncertainty is sufficiently low.