Physical Benchmarking for AI-Generated Cosmic Web
  The potential of deep learning based image-to-image translations has recently
drawn a lot of attention; one intriguing possibility is that of generating
cosmological predictions with a drastic reduction in computational cost. Such
an effort requires optimization of neural networks with loss functions beyond
low-order statistics like pixel-wise mean square error, and validation of
results beyond simple visual comparisons and summary statistics. In order to
study learning-based cosmological mappings, we choose a tractable analytical
prescription - the Zel'dovich approximation - modeled using U-Net, a
convolutional image translation framework. A comprehensive list of metrics is
proposed, including higher-order correlation functions, conservation laws,
topological indicators, dynamical robustness, and statistical independence of
density fields. We find that the U-Net approach does well with some metrics but
has difficulties with others. In addition to validating AI approaches using
rigorous physical benchmarks, this study motivates advancements in
domain-specific optimization schemes for scientific machine learning.
