  The nonzero spectral gap of the original two-dimensional
Affleck-Kennedy-Lieb-Tasaki (AKLT) models has remained unproven for more than
three decades. Recently, Abdul-Rahman et al. [arXiv:1901.09297] provided an
elegant approach and proved analytically the existence of a nonzero spectral
gap for the AKLT models on the decorated honeycomb lattice (for the number $n$
of spin-1 decorated sites on each original edge no less than 3). We perform
calculations for the decorated square lattice and show that the corresponding
AKLT models are gapped if $n\ge 4$. Combining both results, we also show that a
family of decorated hybrid AKLT models, whose underlying lattice is of mixed
vertex degrees 3 and 4, are also gapped for $n\ge 4$. We develop a numerical
approach that extends beyond what was accessible previously. Our numerical
results further improve the nonzero gap to $n\ge 2$, including the
establishment of the gap for $n=2$ in the decorated triangular and cubic
lattices. The latter case is interesting, as this shows the AKLT states on the
decorated cubic lattices are not N\'eel ordered, in contrast to the state on
the undecorated cubic lattice.
