  We present results for the isovector axial vector form factors obtained using
thirteen 2+1+1-flavor highly improved staggered quark (HISQ) ensembles
generated by the MILC collaboration. The calculation of nucleon two- and
three-point correlation functions has been done using Wilson-clover fermions.
In the analysis of these data, we quantify the sensitivity of the results to
strategies used for removing excited state contamination and invoke the
partially conserved axial current relation between the form factors to choose
between them. Our data driven analysis includes removing contributions from
multihadron $N \pi$ states that make significant contributions. Our final
results are: $g_A = 1.292 (53)_\text{stat}\,(24)_\text{sys}$ for the axial
charge; $g_S = 1.085 (50)_\text{stat}\, (103)_\text{sys}$ and $g_T = 0.991
(21)_\text{stat}\, (10)_\text{sys}$ for the scalar and tensor charges; $\langle
r_A^2 \rangle = 0.439 (56)_\text{stat} (34)_\text{sys}$ fm${}^2$ for the mean
squared axial charge radius, $g_P^\ast = 9.03(47)_\text{stat}(42)_\text{sys} $
for the induced pseudoscalar charge; and $g_{\pi NN} =
14.14(81)_\text{stat}(85)_\text{sys}$ for the pion-nucleon coupling. We also
provide a parameterization of the axial form factor $G_A(Q^2)$ over the range
$0 \le Q^2 \le 1$ GeV${}^2$ for use in phenomenology and a comparison with
other lattice determinations. We find that the various lattice data agree
within 10\% but are significantly different from the extraction of $G_A(Q^2)$
from the $\nu$-deuterium scattering data.
