  Ab initio approaches in nuclear theory, such as the no-core shell model
(NCSM), have been developed for approximately solving finite nuclei with
realistic strong interactions. The NCSM and other approaches require an
extrapolation of the results obtained in a finite basis space to the infinite
basis space limit and assessment of the uncertainty of those extrapolations.
Each observable requires a separate extrapolation and most observables have no
proven extrapolation method. We propose a feed-forward artificial neural
network (ANN) method as an extrapolation tool to obtain the ground state energy
and the ground state point-proton root-mean-square (rms) radius along with
their extrapolation uncertainties. The designed ANNs are sufficient to produce
results for these two very different observables in $^6$Li from the ab initio
NCSM results in small basis spaces that satisfy the following theoretical
physics condition: independence of basis space parameters in the limit of
extremely large matrices. Comparisons of the ANN results with other
extrapolation methods are also provided.
