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Abstract
Weighted least squares fitting to a database of quantum mechanical calculations can
determine the optimal parameters of empirical potential models. While algorithms exist
to provide optimal potential parameters for a given fitting database of structures
and their structure property functions, and to estimate prediction errors using Bayesian
sampling, defining an optimal fitting database based on potential predictions remains
elusive. A testing set of structures and their structure property functions provides
an empirical measure of potential transferability. Here, we propose an objective function
for fitting databases based on testing set errors. The objective function allows the
optimization of the weights in a fitting database, the assessment of the inclusion
or removal of structures in the fitting database, or the comparison of two different
fitting databases. To showcase this technique, we consider an example Lennard-Jones
potential for Ti, where modeling multiple complicated crystal structures is difficult
for a radial pair potential. The algorithm finds different optimal fitting databases,
depending on the objective function of potential prediction error for a testing set.