Machine learning approach to pattern recognition in nuclear dynamics from the <i>ab initio</i> symmetry-adapted no-core shell model

A novel machine learning approach is used to provide further insight into atomic nuclei and to detect orderly patterns amid 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 $^{20}\mathrm{Ne}$ ground state, accurately reproduces the probability distribution. The non-negligible configurations predicted by the network provide an important input to the SA-NCSM for reducing ultralarge 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 $^{20\ensuremath{-}42}\mathrm{Mg}$ 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 $^{24}\mathrm{Si}$ and $^{40}\mathrm{Mg}$ of interest to x-ray burst nucleosynthesis, and even of the extremely heavy nuclei such as $^{166,168}\mathrm{Er}$ and $^{236}\mathrm{U}$, that build on first-principles considerations.