  A novel machine learning approach is used to provide further insight into
atomic nuclei and to detect orderly patterns amidst a vast data of large-scale
calculations. The method utilizes a neural network that is trained on ab initio
results from the symmetry-adapted no-core shell model (SA-NCSM) for light
nuclei. We show that the SA-NCSM, which expands ab initio applications up to
medium-mass nuclei by using dominant symmetries of nuclear dynamics, can reach
heavier nuclei when coupled with the machine learning approach. In particular,
we find that a neural network trained on probability amplitudes for $s$-and
$p$-shell nuclear wave functions not only predicts dominant configurations for
heavier nuclei but in addition, when tested for the $^{20}$Ne ground state, it
accurately reproduces the probability distribution. The nonnegligible
configurations predicted by the network provide an important input to the
SA-NCSM for reducing ultra-large model spaces to manageable sizes that can be,
in turn, utilized in SA-NCSM calculations to obtain accurate observables. The
neural network is capable of describing nuclear deformation and is used to
track the shape evolution along the $^{20-42}$Mg isotopic chain, suggesting a
shape-coexistence that is more pronounced toward the very neutron-rich
isotopes. We provide first descriptions of the structure and deformation of
$^{24}$Si and $^{40}$Mg of interest to x-ray burst nucleosynthesis, and even of
the extremely heavy nuclei such as $^{166,168}$Er and $^{236}$U, that build
upon first principles considerations.
