Neural network assisted solution of the Peierls-Boltzmann Equation for phonon transport in semiconductors and insulators*

Unusual heat flow phenomena, such as the hydrodynamic phonon transport, arise out of dissipation-free strong coupling among phonons in crystalline solids, and find applications in thermal cloaking and shielding of semiconductor devices. The Peierls-Boltzmann equation (PBE) governs the coupled dynamics, transport and equilibriation of phonons in these systems and its predictive first principles solution including three- and four-phonon scattering processes, which could serve as a search tool for new materials, has been computationally very expensive, due to its high dimensionality and the need to resolve highly localized, temporally evolving interactions among phonons. To overcome this issue, we present a neural network scheme to solve the PBE, which enables rapid convergence of its steady-state solution and allows for computationally efficient high temporal resolution of localized interactions among phonons under transient transport conditions. We show that, even for materials with complex crystal geometries such as bulk MoS₂, graphite, w-GaN and hBN, the neural network scheme significantly outperforms the conventional iterative solution of the PBE under both steady-state and transient conditions. Our findings highlight the computational advantages of this neural network-based first principles solver for the PBE, which can significantly impact efficient computational search for new materials with exceptional thermal transport properties.