Abstract: The accuracy of classical physical property predictions using molecular dynamics simulations is determined by the quality of the interatomic potentials. Here we introduce a training approach for empirical interatomic potentials (EIPs) which is well suited for capturing phonons and phonon-related properties. Our approach is based on direct comparisons of the second- and third-order irreducible derivatives (IDs) between an EIP and the Born-Oppenheimer potential within density functional theory (DFT) calculations. IDs fully exploit space group symmetry and allow for training without redundant information. We demonstrate the fidelity of our approach in the context of ThO₂ and UO₂, where we optimize parameters of an embedded-atom method potential in addition to core-shell interactions. Our EIPs provide thermophysical properties in good agreement with DFT and outperform widely utilized EIPs for phonon dispersion and thermal conductivity predictions. Reasonable estimates of thermal expansion and formation energies of Frenkel pairs are also obtained.