  The generator coordinate method (GCM) is an important tool of choice for
modeling large-amplitude collective motion in atomic nuclei. The computational
complexity of the GCM increases rapidly with the number of collective
coordinates. It imposes a strong restriction on the applicability of the
method. In this work, we propose a subspace-reduction algorithm that employs
optimal statistical ML models as surrogates for exact quantum-number projection
calculations for norm and Hamiltonian kernels. The model space of the original
GCM is reduced to a subspace relevant for nuclear low energy spectra and the
NME of ground state to ground state $0\nu\beta\beta$ decay based on the
orthogonality condition (OC) and the energy-transition-orthogonality procedure
(ENTROP), respectively. For simplicity, the polynomial ridge regression (RR)
algorithm is used to learn the norm and Hamiltonian kernels of axially deformed
configurations. The efficiency and accuracy of this algorithm are illustrated
for 76Ge and 76Se by comparing results obtained using the optimal RR models to
direct GCM calculations. The low-lying energy spectra of $^{76}$Ge and
$^{76}$Se, as well as the $0\nu\beta\beta$-decay NME between their ground
states, are computed. The results show that the performance of the
GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former
can reproduce the results of the original GCM calculation accurately with a
significantly reduced computational cost.
