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Theoretical uncertainty limits our ability to extract cosmologicalinformation from baryonic fields such as the thermal Sunyaev-Zel'dovich (tSZ)effect. Being sourced by the electron pressure field, the tSZ effect depends onbaryonic physics that is usually modeled by expensive hydrodynamic simulations.We train neural networks on the IllustrisTNG-300 cosmological simulation topredict the continuous electron pressure field in galaxy clusters fromgravity-only simulations. Modeling clusters is challenging for neural networksas most of the gas pressure is concentrated in a handful of voxels and even thelargest hydrodynamical simulations contain only a few hundred clusters that canbe used for training. Instead of conventional convolutional neural net (CNN)architectures, we choose to employ a rotationally equivariant DeepSetsarchitecture to operate directly on the set of dark matter particles. We arguethat set-based architectures provide distinct advantages over CNNs. Forexample, we can enforce exact rotational and permutation equivariance,incorporate existing knowledge on the tSZ field, and work with sparse fields asare standard in cosmology. We compose our architecture with separate,physically meaningful modules, making it amenable to interpretation. Forexample, we can separately study the influence of local and cluster-scaleenvironment, determine that cluster triaxiality has negligible impact, andtrain a module that corrects for mis-centering. Our model improves by 70 % onanalytic profiles fit to the same simulation data. We argue that the electronpressure field, viewed as a function of a gravity-only simulation, has inherentstochasticity, and model this property through a conditional-VAE extension tothe network. This modification yields further improvement by 7 %, it is limitedby our small training set however. (abridged)

Predicting the Thermal Sunyaev-Zel'dovich Field using Modular and Equivariant Set-Based Neural Networks