基于神经评分匹配的暗物质概率映射
Probabilistic Mapping of Dark Matter by Neural Score Matching
摘要：
存在于宇宙大尺度结构中的暗物质是不可见的，但它的存在可以通过它对遥远星系图像的微小引力透镜效应来推断。通过测量大量星系的这种透镜效应，有可能重建天空中暗物质分布的地图。然而，这是一个极具挑战性的逆问题，由于缺失的数据和噪声占主导地位的测量。在这项工作中，我们提出了一种新的方法，通过结合贝叶斯统计，分析物理理论和最近一类基于神经分数匹配的深度生成模型的元素来解决这些逆问题。这种方法允许做以下事情：（1）充分利用解析宇宙学理论来约束解的2pt统计，（2）从宇宙学模拟中学习这种解析先验和完全模拟之间的任何差异，以及（3）从问题的完全贝叶斯后验中获得样本，用于鲁棒的不确定性量化。我们提出了这种方法在哈勃太空望远镜COSMOS领域的第一个深度学习辅助暗物质地图重建上的应用。
英文摘要：
The Dark Matter present in the Large-Scale Structure of the Universe is invisible, but its presence can be inferred through the small gravitational lensing effect it has on the images of far away galaxies. By measuring this lensing effect on a large number of galaxies it is possible to reconstruct maps of the Dark Matter distribution on the sky. This, however, represents an extremely challenging inverse problem due to missing data and noise dominated measurements. In this work, we present a novel methodology for addressing such inverse problems by combining elements of Bayesian statistics, analytic physical theory, and a recent class of Deep Generative Models based on Neural Score Matching. This approach allows to do the following: (1) make full use of analytic cosmological theory to constrain the 2pt statistics of the solution, (2) learn from cosmological simulations any differences between this analytic prior and full simulations, and (3) obtain samples from the full Bayesian posterior of the problem for robust Uncertainty Quantification. We present an application of this methodology on the first deep-learning-assisted Dark Matter map reconstruction of the Hubble Space Telescope COSMOS field.
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