Benchmarking anharmonicity in machine learned interatomic potentials

Machine learning (ML) approaches have recently emerged as powerful tools to probe structure-property relationships in crystals and molecules. Specifically, ML interatomic potentials have been shown to predict ground state properties with near density functional theory (DFT) accuracy at a cost similar to conventional interatomic potential approaches. While ML potentials have been extensively tested across various classes of materials and molecules, there is no clear understanding of how well the anharmonicity of any given system is encoded. Here, we benchmark popular ML interatomic potentials using third and fourth order phonon interactions in fluorite crystals. An anharmonic hamiltonian was constructed from DFT using our highly accurate and efficient irreducible derivative methods, which were then used to train three classes of ML potentials: Gaussian Approximation Potentials, Behler-Parrinello Neural Networks, and Graph Neural Networks. We evaluate their accuracy in not only reproducing anharmonic interaction terms but also in observables such as phonon linewidths and lineshifts. We then present the results of the models trained on a DFT dataset, showing good and reasonable agreement with the DFT computed third and fourth order interactions, respectively. Finally, we discuss strategies to leverage anharmonic terms in the training procedure to improve the accuracy of ML interatomic potentials.