where the total objective function L tot depends on the optimization variables or "mathematical parameters" k, and is equal to the sum of contributions from the parameterization targets L T (k) weighted by w T , plus a regularization term. A parameterization target consists of a collection of weighted least-squares residuals between the force field predictions and a training data set. In this study, all of the liquid thermodynamic properties including surface tension are included in a single target with a weight of 1.0.