Physical Benchmarking for AI-generated Cosmic Web

The potential of deep learning based image-to-image translations have recently drawn a lot of attention in the scientific machine learning community. One such problem of interest is the possibility of generating physically meaningful cosmological data whilst reducing the computational cost involved in high-resolution numerical simulations. Such an effort would require optimization of neural networks beyond low order statistics like pixel-wise mean square error, and validation of results beyond visual comparisons and two-point statistics. In order to study learning-based cosmological evolution, we choose a tractable analytical prescription of Zel'dovich approximation modeled using a convolutional image translation framework called U-Net. A comprehensive list of metrics pertaining to preserving physical laws are proposed, including higher order correlation functions, conservation laws, topological indicators, dynamical robustness and statistical independence of cosmological density fields. In addition to validating AI-generated scientific datasets using rigorous physical benchmarks, this study motivates advancements in domain-specific optimization schemes for scientific machine learning.