RI: III: Medium: Scalable Machine Learning for Automating Scientific Discovery in Astrophysics

这项工作的目的是i）开发和验证新的，有效的机器学习方法，以便以大规模并行和分布式的方式对来自即将到来的天空调查的大规模复杂数据集进行推断和预测，以及ii）使用这些新方法帮助回答宇宙学和天体物理学中的重要基本问题。 这些算法的理论特性也将进行研究。 拟议中的宇宙学和天体物理学应用将包括a）建立恒星光强度信号的概率模型，B）以比传统的N体模拟方法高得多的速度演化宇宙的物质密度，以及c）创建具有所有常见可观测星系属性的“模拟目录”。开发的方法将具有比这里列出的示例更广泛的适用性，无论是天体物理学中的其他问题还是完全不同领域的问题（例如生物信息学，气候学，社会科学），复杂的科学模拟需要大规模的学习方法。在这项工作中开发的软件（包括文档、示例和案例研究）将公开提供。PI还将在他们的研究生和本科生课程材料中包含结果。该提案的目的是开发新的机器学习方法，可以直接在大规模，高维函数和连续分布上工作，作为回归问题的输入或输出，并且可以以大规模并行分布式方式处理大规模科学数据。重要的理论性质，如计算效率，样本的复杂性，泛化精度，一致性，上下限的收敛速度也将进行研究。高斯过程是最常用的非参数贝叶斯函数逼近方法之一。然而，标准的GP方法仅限于最多几千个数据点，并且不适用于大型数据集。GP的核学习是一个更具挑战性的问题。如何为大型数据集扩展GP内核学习方法的问题将作为该项目的一部分得到解决。使用本提案中开发的机器学习方法，将研究以下宇宙学和天体物理学问题：a）将使用具有光谱混合核的可缩放高斯过程来构建来自恒星的光强度信号的概率生成模型，以提取基本属性，例如密度分布。B）新的机器学习算法将用于以比传统的N体模拟方法高得多的速度进化宇宙的物质密度。这将使产生大量宇宙学模拟的全新方式成为可能，以便将宇宙学观测与我们对宇宙的理解进行比较。c）模拟星系表是检验宇宙学分析方法的有力工具，因为模拟中的宇宙学参数是已知的，因此我们恢复它们的能力可以得到完美的检验。对于一个单一的宇宙学模拟，星系的属性和排列并没有完全确定，而是必须以概率的方式添加到暗物质分布中，作为一个额外的建模层，通常有许多参数。 在这项提议中开发的新机器学习工具将用于制作具有所有常见可观测星系属性的“模拟目录”。

The purpose of this work is to i) develop and validate new, efficient machine learning methods for making inferences and predictions in a massively parallel and distributed way on large-scale complex data sets coming from upcoming sky surveys, and ii) help answer important fundamental questions in cosmology and astrophysics using those new methods. Theoretical properties of these algorithms will also be investigated. The proposed cosmology and astrophysics applications will include a) building a probabilistic model for light intensity signals from stars, b) evolving the matter density of the Universe at a speed much higher than the traditional method of N-body simulations, and c) creating "mock catalogs" with all commonly observable galaxy properties. The methods that are developed will have far broader applicability than the examples listed here, both for other problems in astrophysics and problems in completely different domains (e.g. bioinformatics, climatology, social sciences), where complex scientific simulations require large-scale learning methods. The software developed in this work (including documentation, examples, and case studies) will be made publicly available. The PIs will also include the results in their course materials for graduate and undergraduate students.The aim of this proposal is to develop new machine learning methods that can work directly on large-scale, high-dimensional functions and continuous distributions as inputs or outputs in a regression problem, and can process large-scale scientific data in a massively parallel distributed way. Important theoretical properties, such as computational efficiency, sample complexity, generalization accuracy, consistency, lower and upper bounds on the convergence rates will also be investigated. Gaussian processes (GPs) are among the most popular nonparametric Bayesian function approximation methods. However, the standard GP methods are limited to at most a few thousands data points, and not applicable for large datasets. Kernel learning for GPs is an even more challenging problem. The question of how to scale up GP kernel learning methods for large datasets will be addressed as part of this project. Using the machine learning methods developed in this proposal, the following cosmology and astrophysics problems will be investigated: a) Scalable Gaussian processes with spectral mixture kernels will be used to build a probabilistic generative model for light intensity signals from stars to extract fundamental properties such as density profiles. b) New machine learning algorithms will be used to evolve the matter density of the Universe at a speed much higher than the traditional method of N-body simulations. This will enable a completely new way of generating a large number of cosmological simulations in order to compare the cosmological observations to our understanding of the Universe. c) Simulated galaxy catalogs are a powerful tool for testing cosmological analysis methods, since the cosmological parameters in the simulation are known and thus our ability to recover them can be tested perfectly. For a single cosmological simulation, the properties and alignments of galaxies are not fully determined, but rather must be added probabilistically to the dark matter distribution as an extra layer of modeling typically with many parameters. The new machine learning tools developed in this proposal will be used to make "mock catalogs" with all commonly observable galaxy properties.