Multiscale Flow for Robust and Optimal Cosmological Analysis

We propose Multiscale Flow, a generative Normalizing Flow that creates samples and models the field-level likelihood of two dimensional cosmological data such as weak lensing, thus enabling Simulation Based Likelihood Inference. Multiscale Flow uses hierarchical decomposition of cosmological fields via a wavelet basis, and then models different wavelet components separately as Normalizing Flows. This decomposition allows us to separate the information from different scales and identify distribution shifts in the data such as unknown scale-dependent systematics. The resulting likelihood analysis can not only identify these types of systematics, but can also be made optimal, in the sense that the Multiscale Flow can learn the full likelihood at the field without any dimensionality reduction.