AI 中文总结
研究基于卷积神经网络从晚期大尺度结构重建高红移密度场时，输入物理尺度变化。通过N体模拟比较三种方法，发现标准重建后单输入CNN表现最佳，支持解析与数据驱动重建结合，确定了重建后首选输入范围及两种方法优势。
AI 中文摘要
我们研究了用于从晚期大尺度结构重建高红移密度场的卷积神经网络（CNN）方法，重点关注预先应用标准一阶重建时CNN输入的物理尺度如何变化。使用仅含暗物质的N体模拟，我们比较了三种方法：单输入CNN、结合两个物理尺度的双输入CNN，以及应用于标准重建后的密度场的单输入CNN。我们将输入子盒的物理边长在\(L_{sub}\sim38 - 380~h^{-1}Mpc\)范围内变化，同时将其数值大小固定为\(39^3\)体素，以研究空间上下文和分辨率之间的权衡。对于直接应用于演化密度场的CNN，重建在\(L_{sub}\sim150 - 200~h^{-1}Mpc\)时表现最佳。然而，在标准重建之后，首选尺度转移到\(L_{sub}\sim38 - 114~h^{-1}Mpc\)。根据归一化损失、密度概率分布、Kullback-Leibler散度、残差场和傅里叶空间相关性，标准重建后的单输入CNN始终优于未进行标准重建的单输入和双输入CNN。这些结果表明，相干大尺度位移通过微扰重建能更有效地恢复，而CNN更适合对较小尺度上剩余的准线性和非线性演化进行建模。重建后的首选输入范围包括先前混合重建研究中采用的约\(60~h^{-1}Mpc\)的有效感受尺度。因此，我们的发现支持了在解析和数据驱动重建之间基于物理的尺度分离，并证明了结合这两种方法的优势。
英文摘要
We investigate convolutional neural network (CNN) methods for reconstructing the high-redshift density field from late-time large-scale structure, focusing on how the physical scale of the CNN input changes when standard first-order reconstruction is applied beforehand. Using dark-matter-only $N$-body simulations, we compare three approaches: a single-input CNN, a dual-input CNN combining two physical scales, and a single-input CNN applied to the density field after standard reconstruction. We vary the physical side length of the input sub-box over $L_\mathrm{sub}\sim38$-$380~h^{-1}\mathrm{Mpc}$ while keeping its numerical size fixed at $39^3$ voxels, allowing us to examine the trade-off between spatial context and resolution. For the CNN applied directly to the evolved density field, the reconstruction performs best at $L_\mathrm{sub}\sim150$-$200~h^{-1}\mathrm{Mpc}$. After standard reconstruction, however, the preferred scale shifts to $L_\mathrm{sub}\sim38$-$114~h^{-1}\mathrm{Mpc}$. The single-input CNN after standard reconstruction consistently outperforms both the single- and dual-input CNNs without standard reconstruction according to the normalized loss, density probability distribution, Kullback-Leibler divergence, residual field, and Fourier-space correlation. These results indicate that coherent large-scale displacements are more efficiently recovered by perturbative reconstruction, while the CNN is better suited to modelling the remaining quasi-linear and non-linear evolution on smaller scales. The preferred post-reconstruction input range includes the effective receptive scale of approximately $60~h^{-1}\mathrm{Mpc}$ adopted in previous hybrid reconstruction studies. Our findings therefore support a physically motivated separation of scales between analytic and data-driven reconstruction and demonstrate the advantage of combining the two approaches.
Comments10 pages, 5 figures
