  Nonequilibrium dynamics governed by electron-phonon (e-ph) interactions plays
a key role in electronic devices and spectroscopies and is central to
understanding electronic excitations in materials. The real-time Boltzmann
transport equation (rt-BTE) with collision processes computed from first
principles can describe the coupled dynamics of electrons and atomic vibrations
(phonons). Yet, a bottleneck of these simulations is the calculation of e-ph
scattering integrals on dense momentum grids at each time step. Here we show a
data-driven approach based on dynamic mode decomposition (DMD) that can
accelerate the time propagation of the rt-BTE and identify dominant electronic
processes. We apply this approach to two case studies, high-field charge
transport and ultrafast excited electron relaxation. In both cases, simulating
only a short time window of ~10% of the dynamics suffices to predict the
dynamics from initial excitation to steady state using DMD extrapolation.
Analysis of the momentum-space modes extracted from DMD sheds light on the
microscopic mechanisms governing electron relaxation to steady state or
equilibrium. The combination of accuracy and efficiency makes our DMD-based
method a valuable tool for investigating ultrafast dynamics in a wide range of
materials.
