Tensor Learning and Compression of N-Phonon Interactions

Creators: Luo, Yao¹; Mangtani, Dhruv¹; Peng, Shiyu¹; Yao, Jia¹; Kliavinek, Sergei¹; Bernardi, Marco¹

1. California Institute of Technology

Abstract

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 10³–10⁴ 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 ZrO2). 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.

Copyright and License

Acknowledgement

Y. L. thanks Junjie Yang for fruitful discussions. This work was supported by the National Science Foundation under Grant No. OAC-2209262. Y. L. acknowledges support from the Eddleman Fellowship. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 using NERSC award NERSC DDR-ERCAP0026831.

Data Availability

The data that support the findings of this Letter are openly available [59].

Supplemental Material

Supplemental Material:

Supplementary_Information_for_compressing_n_ph_interactions.pdf

Derivations of n-ph interactions and their PCP decomposition, derivations of n-ph anharmonic energy in Eq. (6), computational cost analysis, DFT calculations and IFC generation, comparison of PCP compression and size reduction from symmetry, phonon scattering rate calculations, constrained optimization for acoustic modes, phonon scattering rates for MgO and TiNiSn, thermal conductivity for all studied materials, extrapolation of thermal conductivity to the thermodynamic limit in HgTe, origin of the slow convergence of thermal conductivity for HgTe, number of force constants for 3rd order force constants, and symmetry loss from compression in Si.

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