  We study the nonequilibrium dynamics after an interaction quench in the
two-dimensional Hubbard model using the recently introduced fermionic truncated
Wigner approximation (fTWA). To assess the range of validity of the method in a
systematic way, we consider the SU($N$) Hubbard model with the fermion
degeneracy $N$ as a natural semiclassical expansion parameter. Using both a
numerical and a perturbative analytical approach we show that fTWA is exact at
least up to and including the prethermalization dynamics. We discuss the
limitations of the method beyond this regime.
