can not calculate the gs energy or the gs point proton rms radius for very large $N_{\rm max}$. To obtain the gs energy and the gs point proton rms radius as close as possible to the exact results, the results are extrapolated to the infinite model space. However, it is difficult to construct a simple function with a few parameters to model this type of variation and extrapolate the results to the infinite matrix limit. The advantage of ANN is that it does not need an explicit analytical expression to model the variation of the gs energy or the gs point proton rms radius with respect to $\hbar\Omega$ and $N_{\rm max}$. The *feed-forward* ANN method is very useful to find the converged result at very large $N_{\rm max}$.

In recent years, ANNs have been used in many areas of nuclear physics and high-energy physics. In nuclear physics, ANN models have been developed for constructing a model for the nuclear charge radii [@AKKOYUN:2013], determination of one and two proton separation energies [@ProtonSeparationEnergies:ATHANASSOPOULOS:2004], developing nuclear mass systematics [@NuclearMassSystematics:ATHANASSOPOULOS:2004], identification of impact parameter in heavy-ion collisions [@DAVID:1995; @BASS:1996; @HADDAD:1997], estimating beta decay half-lives [@COSTIRIS:betaDecayHalf-lives:2007] and obtaining potential energy curves [@AKKOYUN:potentialEnergyCurves:2013]. In high-energy physics, 