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

宇宙从物质在空间中几乎均匀分布的简单状态演变而来。在今天，这种物质被非常强烈地聚集成星系、星系团，甚至更大的结构。这种演化受引力和其他过程的支配，比如星系中恒星的形成。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。这些信息很难以目前的形式获取，因为它已经被重力和其他过程扰乱了。这个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在时间上进化时，它们就产生了我们可见的宇宙。最终，这将允许一部关于我们的宇宙的电影，从最初的平滑分布开始，到实际星系的图像结束，比如哈勃深场。这种方法的一个主要好处是，可以简单地从初始条件中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来影响其他出现类似问题的社区，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，以根据星系的空间分布最佳地重建我们宇宙的初始条件。星系是宇宙大尺度结构的主要探测器，正在或将要由斯隆数字巡天(SDSS)、暗能量巡天(DES)、大型天文巡天望远镜(LSST)、暗能量光谱仪(DESI)、欧几里得和广角红外巡天望远镜(WFIRST)等观测到。这个项目将把PI团队开发的分层概率生成模型扩展到星系的建模。该框架试图解决以数据为条件的初始条件的精确概率模型，其过程结合了高维数值优化和分析边际化的元素，以找到最佳解及其协方差矩阵。这项拟议的研究将把这种方法应用于星系红移星表及其周围的暗物质信息，这些信息是从弱透镜中推断出来的。该方法将使用对暗物质和填充在暗物质中的星系的真实模拟和流体模拟来开发，然后应用于真实数据。这项研究将探索在寻找局部和全局最小值的过程中实现快速收敛的最佳方法，并旨在通过为非常高维度的非凸优化开发的工具，对天文学以外的研究领域(例如神经网络)产生更广泛的影响。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.