  In a current-carrying single-molecular junction (SMJ), a hierarchy of hybrid
energy transport processes takes place under a highly nonequilibrium situation,
including energy transfer from electrons to molecular vibrations via
electron-vibration interaction, energy redistribution within different
vibrational modes via anharmonic coupling, and eventual energy transport to
surrounding electrodes. A comprehensive understanding of such processes is a
prerequisite for their potential applications as single-molecular devices. $Ab$
$initio$ current-induced molecular dynamics (MD) is an ideal approach to
address this complicated problem. But the computational cost hinders its usage
in systematic study of realistic SMJs. Here, we achieve orders of magnitude
improvement in the speed of MD simulation by employing machine-learning
potential with accuracy comparable to density functional theory. Using this
approach, we show that SMJs with graphene electrodes generate order of
magnitude less heating than those with gold electrodes. Our work illustrates
the superior heat transport property of graphene as electrodes for SMJs, thanks
to its better phonon spectral overlap with molecular vibrations.
