We propose a lightweight deep convolutional neural network (lCNN) to estimate cosmological parameters from simulated three-dimensional dark matter (DM) halo distributions and associated statistics. The training dataset comprises 2000 realizations of a cubic box with a side length of $1000h^{-1}\mathrm{Mpc}$ and interpolated over a cubic grid of ${300}^3$ voxels, with each simulation produced using ${512}^3$ DM particles and ${512}^3$ neutrinos. Under the flat $\mathrm{\Lambda }\mathrm{CDM}$ model, simulations vary standard six cosmological parameters including ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_b$, $h$, $n_s$, ${\sigma }_8$, and $w$, along with the neutrino mass sum $M_{\nu }$. We find that (i) within the framework of lCNN, extracting large-scale structure information is more efficient from the halo density field compared to relying on the statistical quantities including the power spectrum, the two-point correlation function, and the coefficients from wavelet scattering transform; (ii) combining the halo density field with its Fourier-transformed counterpart enhances predictions, while augmenting the training dataset with measured statistics further improves performance; (iii) achieving high accuracy in inferring ${\mathrm{\Omega }}_m$, $h$, and ${\sigma }_8$ by the neural network model, while being inefficient in predicting ${\mathrm{\Omega }}_b$, $n_s$, $M_{\nu }$, and $w$; and (iv) compared to the simple fully connected network trained with three statistical quantities, our CNN yields statistically reduced errors, showing improvements of approximately 23% for ${\mathrm{\Omega }}_m$, 11% for $h$, 8% for $n_s$, and 21% for ${\sigma }_8$. Additionally, in comparison with the likelihood-based analysis on $P(k)$ data, our CNN provides much tighter constraints on parameters, especially on ${\mathrm{\Omega }}_m$ and ${\sigma }_8$. Our study emphasizes this lCNN-based novel approach in extracting large-scale structure information and estimating cosmological parameters.

中文翻译：

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从暗物质晕密度场推断宇宙学参数的深度学习


我们建议使用 lig $h$ t $w$ 埃格 $h$ t 深度卷积神经网络 $w$ ork (lCNN) 从模拟 t 估计宇宙学参数 $h$ 瑞德一毛钱 $n_s$ 离子暗物质 (DM) 晕分布 $n_s$ 及相关统计数据。训练数据集包含 2000 个实现 $n_s$ 一个边长为的立方体盒子 $1000h^{-1}\mathrm{Mpc}$ 并在立方网格上进行插值 ${300}^3$ 体素，每个模拟都是使用 ${512}^3$ DM 颗粒和 ${512}^3$ 中微子。公寓下 $\mathrm{\Lambda }\mathrm{CDM}$ 模型、模拟会改变标准的六个宇宙学参数，包括 ${\mathrm{\Omega }}_m$ , ${\mathrm{\Omega }}_b$ ，h，ns， ${\sigma }_8$ 、w 以及中微子质量和 $M_{\nu }$ 。我们发现（i）在lCNN的框架内，与依赖功率谱、两点相关函数和小波系数等统计量相比，从晕密度场提取大规模结构信息更有效散射变换； (ii) 将光环密度场与其傅立叶变换对应项相结合可增强预测，同时用测量的统计数据扩充训练数据集可进一步提高性能； (iii) 实现高精度的推断 ${\mathrm{\Omega }}_m$ ， 手 ${\sigma }_8$ 通过神经网络模型，但预测效率低下 ${\mathrm{\Omega }}_b$ , 纳秒, $M_{\nu }$ 、 和 w； (iv) 与使用三个统计量训练的简单全连接网络相比，我们的 CNN 在统计上减少了错误，显示出约 23% 的改进 ${\mathrm{\Omega }}_m$ ，h 为 11%，ns 为 8%，以及 21% ${\sigma }_8$ 。 此外，与基于可能性的分析相比 $P(k)$ 数据，我们的 CNN 对参数提供了更严格的约束，尤其是 ${\mathrm{\Omega }}_m$ 和 ${\sigma }_8$ 。我们的研究强调了这种基于 lCNN 的新颖方法来提取大规模结构信息和估计宇宙学参数。