  We present results on the isoscalar form factors including the disconnected
contributions, as well as on the strange and charm quark form factors. Using
previous results on the isovector form factors, we determine the flavor
decomposition of the nucleon axial form factors. These are computed using an
ensemble of $N_f=2+1+1$ twisted mass fermions simulated with physical values of
quark masses. We investigate the SU(3) flavor symmetry and show that there is
up to 10\% breaking for the axial and up to 50\% for the induced pseudoscalar
form factors. By fitting the $Q^2$-dependence, we determined the corresponding
root mean square radii. The pseudoscalar coupling of the $\eta$ meson and the
nucleon is found to be $g_{\eta NN}=3.7(1.0)(0.7)$, and the Goldberger-Treiman
discrepancy for the octet combination about 50\%.
