  The accuracy of physical property predictions using classical molecular
dynamics simulations is determined by the quality of the empirical interatomic
potentials (EIPs). We introduce a training approach for EIPs, based on direct
comparisons of the second- and third-order interatomic force constants (IFCs)
between EIP and density functional theory (DFT) calculations. This work's
unique aspect is the utilization of irreducible derivatives (IDs) of the total
energy, which leverage on the symmetry of the crystalline structure and provide
a minimal representation of the IFCs. Our approach is tailored toward accurate
predictions of thermal conductivity, thus requiring knowledge of both harmonic
and anharmonic IFCs by matching second- and third-order displacement
derivatives, whereas second-order strain derivatives are needed for determining
the elastic constants. We demonstrate this approach as an efficient and robust
manner in which to train EIPs for predicting phonons and related properties, by
optimizing parameters of an embedded-atom method potential for ThO$_2$, which
is used as a model system for fluorite oxides. Our ID-trained EIP provides
thermophysical properties in great agreement with DFT, and outperforms
previously widely utilized EIP for ThO$_2$ in phonon dispersion and thermal
conductivity calculations. It also provides reasonable estimates of thermal
expansion and the formation energies of simple defects.
