We propose a light-weight deep convolutional neural network (CNN) to estimate the cosmological parameters from simulated 3-dimensional dark matter distributions with high accuracy. The training set is based on 465 realizations of a cubic box with a side length of 256 h⁻¹ Mpc, sampled with 128³ particles interpolated over a cubic grid of 128³ voxels. These volumes have cosmological parameters varying within the flat ΛCDM parameter space of 0.16 ≤ Ω_m ≤ 0.46 and 2.0 ≤ 10⁹A_s ≤ 2.3. The neural network takes as an input cubes with 32³ voxels and has three convolution layers, three dense layers, together with some batch normalization and pooling layers. In the final predictions from the network we find a 2.5% bias on the primordial amplitude σ₈ that cannot easily be resolved by continued training. We correct this bias to obtain unprecedented accuracy in the cosmological parameter estimation with statistical uncertainties of δΩ_m=0.0015 and δσ₈=0.0029, which are several times better than the results of previous CNN works. Compared with a 2-point analysis method using the clustering region of 0–130 and 10–130 h⁻¹ Mpc, the CNN constraints are several times and an order of magnitude more precise, respectively. Finally, we conduct preliminary checks of the error-tolerance abilities of the neural network, and find that it exhibits robustness against smoothing, masking, random noise, global variation, rotation, reflection, and simulation resolution. Those effects are well understood in typical clustering analysis, but had not been tested before for the CNN approach. Our work shows that CNN can be more promising than people expected in deriving tight cosmological constraints from the cosmic large scale structure.

我们提出了一种轻量级的深度卷积神经网络（CNN），可以从模拟的3维暗物质分布中高精度地估计宇宙学参数。该训练集基于边长为256 h ^-1 Mpc的立方盒的465个实现，并在128 ³个体素的立方网格上插值了128 ^3个粒子。这些卷有宇宙学参数的0.16≤Ω扁平ΛCDM参数空间内变化的_米≤0.46和2.0≤10 ⁹甲_小号≤2.3。神经网络以32 ³为输入立方体体素并具有三个卷积层，三个密集层以及一些批处理规范化和合并层。在从网络的最终预测，我们发现在原始幅度的2.5％偏差σ ₈不能轻易被持续的培训解决。我们矫正这种偏差，以获得在宇宙学参数估计前所未有的精度与统计不确定性δ Ω_米= 0.0015和ΔΣ ₈ = 0.0029，这比以前的作品CNN结果的几倍。与使用0-130和10-130 h ^-1的聚类区域的两点分析方法相比Mpc，CNN约束分别是原来的几倍和一个数量级。最后，我们对神经网络的容错能力进行了初步检查，发现它表现出了对平滑，屏蔽，随机噪声，全局变化，旋转，反射和仿真分辨率的鲁棒性。这些效果在典型的聚类分析中已广为人知，但之前尚未经过CNN方法的测试。我们的工作表明，从宇宙大尺度结构中得出严格的宇宙学约束时，CNN可能比人们期望的更有希望。