  The modeling of nuclear reactions and radioactive decays in astrophysical or
earth-based conditions requires detailed knowledge of the masses of essentially
all nuclei. Microscopic mass models based on nuclear energy density functionals
(EDFs) can be descriptive and used to provide this information. The concept of
intrinsic symmetry breaking is central to the predictive power of EDF
approaches, yet is generally not exploited to the utmost by mass models because
of the computational demands of adjusting up to about two dozen parameters to
thousands of nuclear masses. We report on a first step to bridge the gap
between what is presently feasible for studies of individual nuclei and
large-scale models: we present a new Skyrme-EDF-based model that was adjusted
using a three-dimensional coordinate-space representation, for the first time
allowing for both axial and triaxial deformations during the adjustment
process. To compensate for the substantial increase in computational cost
brought by the latter, we have employed a committee of multilayer neural
networks to model the objective function in parameter space and guide us
towards the overall best fit. The resulting mass model BSkG1 is computed with
the EDF model independently of the neural network. It yields a root mean square
(rms) deviation on the 2457 known masses of 741 keV and an rms deviation on the
884 measured charge radii of 0.024 fm.
