Forthcoming cosmological imaging surveys, such as the Rubin Observatory LSST, require large-scale simulations encompassing realistic galaxy populations for a variety of scientific applications. Of particular concern is the phenomenon of intrinsic alignments (IA), whereby galaxies orient themselves towards overdensities, potentially introducing significant systematic biases in weak gravitational lensing analyses if they are not properly modeled. Due to computational constraints, simulating the intricate details of galaxy formation and evolution relevant to IA across vast volumes is impractical. As an alternative, we propose a Deep Generative Model trained on the IllustrisTNG-100 simulation to sample 3D galaxy shapes and orientations to accurately reproduce intrinsic alignments along with correlated scalar features. We model the cosmic web as a set of graphs, each graph representing a halo with nodes representing the subhalos/galaxies. The architecture consists of a SO(3) $\times$ $\mathbb{R}^n$ diffusion generative model, for galaxy orientations and $n$ scalars, implemented with E(3) equivariant Graph Neural Networks that explicitly respect the Euclidean symmetries of our Universe. The model is able to learn and predict features such as galaxy orientations that are statistically consistent with the reference simulation. Notably, our model demonstrates the ability to jointly model Euclidean-valued scalars (galaxy sizes, shapes, and colors) along with non-Euclidean valued SO(3) quantities (galaxy orientations) that are governed by highly complex galactic physics at non-linear scales.

本研究针对传统星系模拟在处理星系内在排列（IA）现象中存在的系统性偏差问题，通过使用深度生成模型与IllustrisTNG-100模拟相结合，提出了一种新方法来准确再现星系形状和方向。研究结果表明，该模型能够在统计上与参考模拟一致地学习和预测星系的取向及相关特征，具有重要的潜在影响。 

几何深度学习在星系-光晕连接中的应用：星系内在排列的案例研究