The training set includes multiple configurations corresponding to bulk and surface of the solid and liquid phases. Initial configurations were chosen from previous work and then augmented by an iterative trial and error approach to improve the description of the interface in simulation cells tractable with DFT. and theoretical width for Cu results from a fit via an error function in one case and a Gaussian in the other. We note that fitting the resulting electron density with an error function reproduces the choice of σ =1.0 Å for Cu in the experiment.