  We present a cosmic density field reconstruction method that augments the
traditional reconstruction algorithms with a convolutional neural network
(CNN). Following Shallue $\&$ Eisenstein (2022), the key component of our
method is to use the $\textit{reconstructed}$ density field as the input to the
neural network. We extend this previous work by exploring how the performance
of these reconstruction ideas depends on the input reconstruction algorithm,
the reconstruction parameters, and the shot noise of the density field, as well
as the robustness of the method. We build an eight-layer CNN and train the
network with reconstructed density fields computed from the Quijote suite of
simulations. The reconstructed density fields are generated by both the
standard algorithm and a new iterative algorithm. In real space at $z=0$, we
find that the reconstructed field is $90\%$ correlated with the true initial
density out to $k\sim 0.5 h{\rm Mpc}^{-1}$, a significant improvement over
$k\sim 0.2 h{\rm Mpc}^{-1}$ achieved by the input reconstruction algorithms. We
find similar improvements in redshift space, including an improved removal of
redshift space distortions at small scales. We also find that the method is
robust across changes in cosmology. Additionally, the CNN removes much of the
variance from the choice of different reconstruction algorithms and
reconstruction parameters. However, the effectiveness decreases with increasing
shot noise, suggesting that such an approach is best suited to high density
samples. This work highlights the additional information in the density field
beyond linear scales as well as the power of complementing traditional analysis
approaches with machine learning techniques.
