CDS&E: Reconstruction of universe's initial conditions with galaxies

宇宙是从物质在空间中几乎均匀分布的简单状态演化而来的。在今天，物质非常强烈地聚集成星系，星系团，甚至更大的结构。这种演化受重力和其他过程（如星系中恒星的形成）的控制。星系分布中隐藏着大量关于宇宙起源、内容和未来演化的信息。 这些信息很难以今天的形式获得，因为它已经被重力和其他过程打乱了。该项目的目标是使用模拟来重建我们宇宙的初始条件。当它们按照已知的物理定律及时演化时，它们就产生了我们可见的宇宙。最终，这将使我们的宇宙从最初的平滑分布开始，以实际星系的图像（如哈勃深场）结束。这种方法的一个主要好处是，可以从初始条件中简单地提取关于我们宇宙的信息。 更广泛地说，该项目的目的是通过开发的方法和工具影响其他出现类似问题的社区，例如机器学习 该项目的主要目标是开发和应用一套新的理论和计算工具，包括新的统计方法，算法和计算实现，以最佳方式从星系的空间分布重建我们宇宙的初始条件。伽利略是宇宙大尺度结构的主要探测器，这些结构已经或将要通过诸如斯隆数字巡天（SDSS）、暗能量巡天（DES）、大型综合巡天望远镜（LSST）、暗能量光谱仪（DESI）、欧几里得和宽视场红外巡天望远镜（WFIRST）等巡天观测。该项目将扩展PI团队开发的分层概率生成模型，用于星系建模。该框架试图解决一个精确的概率模型的初始条件，是以数据为条件的过程，结合元素的数值优化在高维和分析边缘化，以找到最佳的解决方案和他们的协方差矩阵。拟议中的研究将把这种方法应用于星系红移目录和从弱透镜推断出的周围暗物质信息。在应用于真实的数据之前，将使用对暗物质和暗物质中星系的真实模拟和水模拟来开发该方法。 本研究将探讨最佳的方法，以实现快速收敛，在寻找当地和全球最低，并旨在产生更广泛的影响，以研究领域（例如神经网络）在天文学以外的工具开发的非该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响进行评估，被认为值得支持审查标准。

The universe evolved from a simple state where matter was almost uniformly distributed in space. In the present day the matter is very strongly clustered into galaxies, clusters of galaxies, and even larger structures. This evolution is governed by gravity and by additional processes such as formation of stars in galaxies. There is enormous amount of information about the universe origins, content, and future evolution hidden in the galaxy distribution. This information is difficult to access in the present-day form because it has been scrambled by gravity and other processes. The goal of this project is to use simulations to reconstruct the initial conditions of our universe. When these are evolved in time with known laws of physics, they give rise to our visible universe. Ultimately this will allow a movie to made of our universe starting from the initial smooth distribution and ending in images of actual galaxies such as the Hubble Deep Field. A major benefit of this method is that information about our universe can be simply extracted from the initial conditions. More broadly, an aim of this project is to impact other communities where similar problems arise such as machine learning via the methods and tools developed The primary goal of this project is to develop and apply a new set of theoretical and computational instruments, including new statistical methods, algorithms, and computational implementations, to optimally reconstruct the initial condition of our universe from the spatial distribution of galaxies. Galaxies are a primary probe of the large scale structure of the universe that are or will be observed by surveys such as the Sloan Digital Sky Survey (SDSS), the Dark Energy Survey (DES), the Large Synoptic Survey Telescope (LSST), the Dark Energy Spectroscopic Instrument (DESI), EUCLID and the Wide Field Infrared Survey Telescope (WFIRST). This project will extend a hierarchical probabilistic generative model developed by the PI's team to the modelling of galaxies. The framework attempts to solve an exact probabilistic model for the initial conditions that is conditioned on the data with a process that combines elements of numerical optimization in high dimensions and analytic marginalization to find the best solution and their covariance matrix. The proposed research will apply this method to galaxy redshift catalogs and their surrounding dark matter information inferred from weak lensing. The method will be developed using realistic simulations of both dark matter and of galaxies populated in the dark matter and hydro simulations, before being applied to real data. This research will explore best methods to achieve fast convergence in the search for local and global minimum and aims to have an impact more broadly to research areas (e.g. neural networks) outside astronomy in the tools developed for non-convex optimization in very high dimensions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.