Tensor Learning and Compression of N-Phonon Interactions

Phonon interactions from lattice anharmonicity govern thermal properties and heat transport in materials. These interactions are described by nth order interatomic force constants (nIFCs), which can be viewed as high-dimensional tensors correlating the motion of n atoms, or equivalently encoding n-phonon scattering processes in momentum space. Here, we introduce a tensor decomposition to efficiently compress nIFCs for arbitrary order n. Using tensor learning, we find optimal low-rank approximations of nIFCs by solving the resulting optimization problem. Our approach reveals the inherent low dimensionality of phonon-phonon interactions and allows compression of the three- and four-IFC tensors by factors of up to 10^{3}-10^{4} while retaining high accuracy in calculations of phonon scattering rates and thermal conductivity. Calculations of thermal conductivity using the compressed nIFCs achieve a speedup by nearly 3 orders of magnitude with >98% accuracy relative to the reference uncompressed solution. These calculations include both three- and four-phonon scattering and are shown for a diverse range of materials (Si, HgTe, MgO, TiNiSn, and ZrO_{2}). In addition to accelerating state-of-the-art thermal transport calculations, the method shown here paves the way for modeling strongly anharmonic materials and higher-order phonon interactions.