Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis
Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis
复制标题
用于最佳宇宙学分析的平移和旋转等变归一化流 (TRENF)
DOI：
10.1093/mnras/stac2010
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发表时间：
2022
影响因子：
4.8
通讯作者：
Seljak, Uroš
中科院分区：
文献类型：
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作者：
Dai, Biwei;Seljak, Uroš
我们的宇宙是均匀和各向同性的，它的微扰服从平移和旋转对称。在这项工作中，我们开发了平移和旋转等变归一化流（TRENF），这是一种生成归一化流（NF）模型，它明确地结合了这些对称性，通过一系列基于傅里叶空间的卷积和逐像素的非线性变换来定义数据的可能性。TRENF可以直接访问作为标记函数的高维数据似然（x|y），例如宇宙学参数。与基于汇总统计的传统分析相比，NF方法没有信息损失，因为它保留了数据的全部维度。在高斯随机场上，TRENF似然与解析表达式吻合较好，使标签中的Fisher信息含量饱和。在n体模拟的非线性宇宙过密度场中，TRENF在标准功率谱汇总统计的功率约束方面取得了显著的进步。TRENF也是数据的生成模型，我们表明TRENF样本与它所训练的theN-body模拟非常吻合，并且数据的逆映射在视觉上和各种汇总统计上都与高斯白噪声非常吻合：当这完全实现时，结果（x|y）似然分析变得最优。最后，我们对该模型进行了推广，可以处理破坏数据对称性的影响，例如调查掩码，它可以对没有周期边界的数据进行似然分析。
Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihoodp(x|y) as a function of the labelsy, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labelsy. On non-linear cosmological overdensity fields fromN-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with theN-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resultingp(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.