The Bayesian approach for feed-forward neural networks has been applied to the extraction of the nucleon axial form factor from the neutrino-deuteron scattering data measured by the Argonne National Laboratory bubble chamber experiment. This framework allows to perform a modelindependent determination of the axial form factor from data. When the low 0.05 < Q 2 < 0.10 GeV 2 data are included in the analysis, the resulting axial radius disagrees with available determinations. Furthermore, a large sensitivity to the corrections from the deuteron structure is obtained. In turn, when the low-Q 2 region is not taken into account with or without deuteron corrections, no significant deviations from previous determinations have been observed. A more accurate determination of the nucleon axial form factor requires new precise measurements of neutrino-induced quasielastic scattering on hydrogen and deuterium.