Data-driven solution of the real-time Boltzmann transport equation: speeding up and finding patterns in first-principles calculations of nonequilibrium dynamics

The Boltzmann transport equation (BTE) is a convenient framework for studies of nonequilibrium dynamics in materials. We have recently shown that solving the real-time BTE (rt-BTE) by time-stepping the electron and phonon occupations enables first-principles studies of nonequilibrium dynamics of coupled electrons and phonons [1,2]. Variants of this formalism include ab initio electron-phonon (e-ph) and/or phonon-phonon (ph-ph) interactions, external electric fields, and even excitonic effects. However, a bottleneck of these methods is computing the BTE collision integrals, which requires dense momentum grids, leading to high computational cost even for simple materials.

In this talk, we present a data-driven approach based on dynamic mode decomposition (DMD) to accelerate the solution of the electronic rt-BTE. This approach enables calculations of nonequilibrium electron populations and steady-state solution in external fields with order-of-magnitude reduction in computational cost while fully preserving the accuracy. Analysis of the leading modes extracted from DMD sheds light on the dominant scattering and relaxation mechanisms. We show illustrative examples of such data-driven electron dynamics calculations and discuss their implementation in the Perturbo code. We conclude by discussing extensions for data-driven nonequilibrium phonon dynamics.

[1] I. Maliyov, J. Park, M. Bernardi, Phys. Rev. B 104, L100303 (2021)

[2] X. Tong, M. Bernardi, Phys. Rev. Research, 3 (2021)