Predicting the thermal Sunyaev–Zel’dovich field using modular and equivariant set-based neural networks

Abstract

Theoretical uncertainty limits our ability to extract cosmological information from baryonic fields such as the thermal Sunyaev-Zel’dovich (tSZ) effect. Being sourced by the electron pressure field, the tSZ effect depends on baryonic physics that is usually modeled by expensive hydrodynamic simulations. We train neural networks on the IllustrisTNG-300 cosmological simulation to predict the continuous electron pressure field in galaxy clusters from gravity-only simulations. Modeling clusters is challenging for neural networks as most of the gas pressure is concentrated in a handful of voxels and even the largest hydrodynamical simulations contain only a few hundred clusters that can be used for training. Instead of conventional convolutional neural net (CNN) architectures, we choose to employ a rotationally equivariant DeepSets architecture to operate directly on the set of dark matter particles. We argue that set-based architectures provide distinct advantages over CNNs. For example, we can enforce exact rotational and permutation equivariance, incorporate existing knowledge on the tSZ field, and work with sparse fields as are standard in cosmology. We compose our architecture with separate, physically meaningful modules, making it amenable to interpretation. For example, we can separately study the influence of local and cluster-scale environment, determine that cluster triaxiality has negligible impact, and train a module that corrects for mis-centering. Our model improves by 70% on analytic profiles fit to the same simulation data. We argue that the electron pressure field, viewed as a function of a gravity-only simulation, has inherent stochasticity, and model this property through a conditional-VAE extension to the network. This modification yields further improvement by 7%, it is limited by our small training set however. We envision that our method will prove useful in problems beyond the specific one considered here.

GREENER principles for environmentally sustainable computational science

“…Some authors already do this voluntarily (for example, refs. [54][55][56][57][58][59], mostly in bioinformatics and machine learning so far, but there is potential to expand it to other areas of computational science. In some instances, showing that a new tool is greener can be an argument in support of a new method 60 .…”

Mangrove: Learning Galaxy Properties from Merger Trees

“…In this work, we present a new method for learning this highly nontrivial mapping, using the natural choice for learning on merger trees, a graph neural network (GNN). GNNs have lately been demonstrated to work extremely well at modeling various problems in astrophysics (e.g., Cranmer et al 2019Cranmer et al , 2020Cranmer et al , 2021aCranmer et al , 2021bVillanueva-Domingo et al 2022;Lemos et al 2022;Thiele et al 2022). This choice of model allows us to include the full merger history as recorded in the merger tree, since the merger tree can naturally be encoded as a graph.…”