<p>Phonon interactions from lattice anharmonicity govern thermal properties and heat transport in materials.<br>These interactions are described by n-th order interatomic force constants (n-IFCs), which can be viewed as high-dimensional tensors correlating the motion of n atoms, or equivalently encoding n-phonon scattering processes in momentum space. <br>Here, we introduce a tensor decomposition to efficiently compress n-IFCs for arbitrary order n. <br>Using tensor learning, we find optimal low-rank approximations of n-IFCs by solving the resulting optimization problem. <br>Our approach reveals the inherent low dimensionality of phonon-phonon interactions and allows compression of the 3 and 4-IFC tensors by factors of up to 10^3-10^4 while retaining high accuracy in calculations of phonon scattering rates and thermal conductivity. <br>Calculations of thermal conductivity using the compressed n-IFCs achieve a speed-up by nearly three orders of magnitude with >98% accuracy relative to the reference uncompressed solution. These calculations include both 3- and 4-phonon scattering and are shown for a diverse range of materials (Si, HgTe, MgO, TiNiSn and monoclinic ZrO<sub>2</sub>). <br>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.</p>
<p>This data contains the phonon scattering rates data with full and compressed phonon-phonon interactions. The data corresponds to Figure 3 in the paper and includes information on the phonon scattering rates for two materials: silicon and HgTe.</p>
<p> </p>
