Enabling KARMMA as a Tool of Precision Cosmology

重力会使光线弯曲。因此，在图像前面增加质量会扭曲图像。测量这些扭曲使我们能够确定所添加的质量的分布。鲁宾天文台的时空遗产调查(LSST)将利用这种引力透镜效应来测量暗物质在宇宙中的分布，目的是更好地了解是什么驱动了我们宇宙的加速膨胀。传统上，这种类型的分析是通过计算汇总统计数据来完成的：想象一下，拿一张物质密度图，然后通过比方说，峰之间的平均距离来总结所有信息。这种“压缩”是必要的：预测汇总统计数据是“容易的”，而预测暗物质图则很难。亚利桑那大学的科学家试图将机器学习技术与最近的发展相结合，从大规模地图本身中提取宇宙学信息。这样做将确保以最佳方式提取数据中包含的宇宙学信息。作为该项目的一部分，PI将作为亚利桑那大学新开发的时间步长研究学徒计划的志愿者教员，培训本科生研究和编码技能，这将提高他们获得暑期研究实习的能力，无论是REU计划还是行业。从弱透镜测量数据中提取宇宙学信息的标准方法依赖于剪切关联函数。然而，今天的物质密度场是非高斯的，这一事实使这种方法变得次优：如果它的非高斯特征中包含的信息能够被提取出来，来自宇宙剪切实验的宇宙学约束可以改善两倍或更多。基于领域的推理已经成为实现这一目标的明显选择。该小组提议在KARMMA大规模测绘算法的成功基础上，开发第一个实用和准确的基于现场的推理框架。这项工作将克服通过使用模拟非线性增长的近似方法来运行暗物质模拟的需要。具体地说，该计划是：1)扩展KARMMA框架，以实现层析质量图和宇宙采样；以及2)训练卷积神经网络，将KARMMA对数正态图扰动为模拟质量的图。后验数据的有效采样将通过使用哈密顿马尔可夫链来实现。然后，完整的推理框架将使用模拟数据集进行验证。这一裁决反映了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。

Gravity bends light. Consequently, adding mass in front of an image will distort the image. Measuring these distortions allow us to determine the distribution of mass that was added. The Rubin Observatory Legacy Survey of Space and Time (LSST) will use this gravitational lensing effect to measure the distribution of dark matter in the Universe, with the goal of better understanding what drives the accelerated expansion of our Universe. Traditionally, this type of analysis is done by calculating summary statistics: think of taking a map of the matter density, and summarizing all that information by, say, the average distance between peaks. This “compression” is done by necessity: predicting summary statistics is “easy”, whereas predicting dark matter maps is hard. Scientists at the University of Arizona seek to combine machine learning techniques with recent developments to extract cosmological information from the mass maps themselves. Doing so will ensure that the cosmological information contained in the data will be extracted in an optimal way. As part of this project, the PI will act as a volunteer faculty member in the newly developed TIMESTEP research apprenticeship program at the University of Arizona, training undergraduates on research and coding skills that will improve their ability to secure summer research internships, be it REU programs or in industry.The standard approach for extracting cosmological information from weak lensing survey data relies on the shear correlation function. However, the fact that the matter density field today is non-gaussian renders this approach sub-optimal: if the information contained in its non-gaussian features could be extracted, the cosmological constraints from cosmic shear experiments could be improved by a factor of two or more. Fields-based inference has emerged as the obvious choice for realizing this goal. The team proposes to build on the success of the KARMMA mass mapping algorithm to develop the first practical and accurate field-based inference framework. This work will overcome the need to run dark matter simulations by using approximate methods for modeling non-linear growth. Specifically, the plan is to: 1) extend the KARMMA framework to enable tomographic mass map and cosmological sampling; and 2) train a convolutional neural network to perturb the KARMMA lognormal maps into simulation-quality maps. Efficient sampling of the posterior will be achieved through the use of Hamiltonian Markov Chains. The full inference framework will then be validated using simulated data sets.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.