The potential of deep learning-based image-to-image translations has recently attracted significant attention, and serves as a potentially powerful alternative to cosmological simulations, useful in contexts such as covariance studies, investigations of systematics, and cosmological parameter inference. To investigate various aspects of learning-based cosmological mappings, we choose two approaches for generation of cosmological matter fields as datasets: the analytical prescription provided by the Zel’dovich approximation, and the numerical N-body Particle-Mesh method. A comprehensive list of metrics is considered, including higher-order correlation functions, conservation laws, topological indicators, and statistical independence of density fields. We find that a U-Net approach performs well only for some of these physical metrics. In addition, we develop strategies to expand the available dynamical range of …