pattern shows a reduction in the spacing between successive curves and flattening of the curves as $N_{\rm max}$ increases. The gs energy provided by the ANN decreases monotonically with increasing $N_{\rm max}$ at all values of $\hbar\Omega$. This demonstrates that the ANN is successfully simulating what is expected from theoretical physics. That is, in theoretical physics the energy variational principle requires that the gs energy behaves as a non-increasing function of increasing matrix dimensionality at fixed $\hbar\Omega$ and, furthermore, matrix dimension increases with increasing $N_{\rm max}$.

![Calculated and predicted gs energy of $^6\mathrm{Li}$ as a function of $\hbar\Omega$ at selected $N_{\rm max}$ values. []{data-label="fig:Li6_gs_energy"}](Li6_gs_energy_best-eps-converted-to.pdf){width="\linewidth"}

To illustrate the ANN prediction accuracy, the NCSM calculation results and the corresponding ANN prediction results of the gs energy of $^6\mathrm{Li}$ are presented in Figure \[fig:Li6\_gs\_energy\_cp\] as a function of $\hbar\Omega$ at $N_{\rm max} = 12, 14, 16$, and $18$. The dashed curves connect the NCSM calculation results using the Daejeon16 NN interaction and the solid curves link the ANN prediction results. The nearly converged result predicted by ANN is also shown above the horizontal axis at $N_{\rm max} = 70$. Figure \[fig:Li6\_gs\_energy\_cp\] shows good agreement between the calculated NCSM results and the ANN predictions 