Cosmology at the Field Level with Probabilistic Machine Learning

The large-scale structure in cosmology is highly non-Gaussian at late times and small length scales, making it difficult to describe analytically. Parameter inference, data reconstruction, and data generation tasks in cosmology are greatly aided by various machine learning models. In order to retain as much information as possible while solving these problems, this work operates at the field level, rather than at the level of summary statistics. The probability density function of the large-scale structure is learned with normalizing flows, a class of probabilistic generative models. Normalizing flows learn the transformation from a simple base distribution to a more complicated distribution, much like the matter content evolved to its present day complexities from a Gaussian field at early times. While the normalizing flows have accurately modelled 2-dimensional projections of the matter content, we find that denoising diffusion models are well-suited for volumetric data. A super-resolution emulator is developed for cosmological simulation volumes, generating high-resolution baryonic simulation volumes conditional on low-resolution dark matter simulations. The super-resolution emulator is trained to perform outpainting, and can thus upgrade very large cosmological volumes from low-resolution to high-resolution using an iterative outpainting procedure.