标题： 基于神经分数匹配的暗物质概率测绘 显示英文标题

标题： Probabilistic Mapping of Dark Matter by Neural Score Matching

摘要： 宇宙大尺度结构中存在的暗物质是不可见的，但可以通过它对遥远星系图像产生的微小引力透镜效应推断其存在。 通过测量大量星系上的这种透镜效应，可以重建天空中暗物质分布的地图。 然而，由于数据缺失和噪声主导的测量，这代表了一个极其具有挑战性的逆问题。 在这项工作中，我们提出了一种新颖的方法来解决这类逆问题，结合了贝叶斯统计、解析物理理论以及基于神经网络评分匹配的最新深度生成模型。 这种方法可以实现以下几点：（1）充分利用解析宇宙学理论来约束解的二阶统计量；（2）从宇宙学模拟中学习解析先验与完整模拟之间的差异；（3）从问题的完整贝叶斯后验中获取样本以进行稳健的不确定性量化。 我们展示了该方法在哈勃太空望远镜COSMOS区域暗物质图重建中的首次深度学习辅助应用。 显示英文摘要

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.