  We formalized the nuclear mass problem in the inverse problem framework. This
approach allows us to infer the underlying model parameters from experimental
observation, rather than to predict the observations from the model parameters.
The inverse problem was formulated for the numericaly generalized the
semi-empirical mass formula of Bethe and von Weizs\"{a}cker. It was solved in
step by step way based on the AME2012 nuclear database.
  The solution of the overdetermined system of nonlinear equations has been
obtained with the help of the Aleksandrov's auto-regularization method of
Gauss-Newton type for ill-posed problems. In the obtained generalized model the
corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50,
82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic
numbers as well on the asymptotic boundaries of their influence. These results
help us to evaluate the borders of the nuclear landscape and show their limit.
The efficiency of the applied approach was checked by comparing relevant
results with the results obtained independently.
