  Accurately predicting carrier mobility in strongly anharmonic solids
necessitates a precise characterization of lattice dyndamics as a function of
temperature. We achieve consistency with experimental electron mobility data
for bulk KTaO$_3$ and SrTiO$_3$ above 150 K by refining the Boltzmann transport
equations. This refinement includes incorporating temperature-dependent
anharmonic phonon eigenfrequencies and eigenmodes into the electron-phonon
interaction tensor, while maintaining the derivatives of the Kohn-Sham
potential as computed in density functional perturbation theory. Using
efficient machine-learned force fields and the stochastic self-consistent
harmonic approximation, we accurately compute the dynamical matrices. At room
temperature, the calculated mobility for SrTiO$_3$ exceeds experimental values
by an order of magnitude, whereas the overestimation for KTaO$_3$ is way less
pronounced. This discrepancy is explained through the more significant electron
mass renormalization near the conduction band bottom due to anharmonic
electron-phonon coupling and the presence of local disorder in SrTiO$_3$.
