  The origin of `invisible' axion in four dimensional effective beyond-standard
models from string compactification is discussed and its refined passover
through the QCD phase transition is presented toward a reliable estimate of the
current axion energy density in terms of the initial misalignment angle
$\bar{\theta}_1$. The explicit examples are presented in a flipped SU(5) GUT
model. This allows to introduce a flavor symmetry through string
compactification, and hence we also comment on the source of flavor symmetries
from string compactification and attempts to fit the resulting Yukawa couplings
to the observed Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata
matrices.
