标题： 一个用于从星系团和星系 catalogue 预测$Ω_{\rm m}$的通用方程 显示英文标题

标题： A universal equation to predict $Ω_{\rm m}$ from halo and galaxy catalogues

摘要： 我们发现了可以从前 Halo 和星系目录的位置和速度模量推断出$\Omega_{\rm m}$值的解析方程。 这些方程通过结合定制的图神经网络（GNN）架构与符号回归方法推导而来。 我们首先使用 Gadget N 体模拟中的暗物质晕来训练 GNN，以执行字段级无偏似然推理，并表明我们的模型可以从用六种不同代码运行的数千个 N 体模拟的晕目录中以$\sim6\%$的精度推断出$\Omega_{\rm m}$：Abacus、CUBEP$^3$M、Gadget、Enzo、PKDGrav3 和 Ramses。 通过对构成 GNN 的各个部分应用符号回归，我们得出了可以从所有上述代码运行的模拟的晕目录中预测$\Omega_{\rm m}$的方程，其准确性与 GNN 相当。 我们表明，通过调整单个自由参数，我们的方程还可以从前沿流体力学模拟的 CAMELS 项目中数千个具有不同天体物理模型的星系目录中推断出$\Omega_{\rm m}$的值，这些模拟使用了五种采用不同子网格物理的不同代码：IllustrisTNG、SIMBA、Astrid、Magneticum 和 SWIFT-EAGLE。 此外，当在覆盖参数空间广阔区域并采样 5 个宇宙学和 23 个天体物理学参数变化的模拟的星系目录上进行测试时，这些方程的表现也很出色。 我们推测，这些方程可能反映了通用示踪粒子相空间分布与$\Omega_{\rm m}$之间存在基本物理关系，这种关系不受星系形成物理过程的影响，甚至在小至$10~h^{-1}{\rm kpc}$的尺度上也是如此。 显示英文摘要

摘要： We discover analytic equations that can infer the value of $\Omega_{\rm m}$ from the positions and velocity moduli of halo and galaxy catalogues. The equations are derived by combining a tailored graph neural network (GNN) architecture with symbolic regression. We first train the GNN on dark matter halos from Gadget N-body simulations to perform field-level likelihood-free inference, and show that our model can infer $\Omega_{\rm m}$ with $\sim6\%$ accuracy from halo catalogues of thousands of N-body simulations run with six different codes: Abacus, CUBEP$^3$M, Gadget, Enzo, PKDGrav3, and Ramses. By applying symbolic regression to the different parts comprising the GNN, we derive equations that can predict $\Omega_{\rm m}$ from halo catalogues of simulations run with all of the above codes with accuracies similar to those of the GNN. We show that by tuning a single free parameter, our equations can also infer the value of $\Omega_{\rm m}$ from galaxy catalogues of thousands of state-of-the-art hydrodynamic simulations of the CAMELS project, each with a different astrophysics model, run with five distinct codes that employ different subgrid physics: IllustrisTNG, SIMBA, Astrid, Magneticum, SWIFT-EAGLE. Furthermore, the equations also perform well when tested on galaxy catalogues from simulations covering a vast region in parameter space that samples variations in 5 cosmological and 23 astrophysical parameters. We speculate that the equations may reflect the existence of a fundamental physics relation between the phase-space distribution of generic tracers and $\Omega_{\rm m}$, one that is not affected by galaxy formation physics down to scales as small as $10~h^{-1}{\rm kpc}$.