Reduced Basis for Gravitational Waves: Select, Solve, Represent, Predict

由中子星、黑洞或混合对组成的双星系统预计将成为下一代先进的地球引力波探测器（如先进的LIGO）的最重要来源。有许多模型可以用来描述这样的系统，例如后牛顿模型、唯象模型、有效单体模型，以及完整爱因斯坦方程的数值模拟（数值相对论领域）。不管用什么模型来描述它，这个问题都有相当大的维度。粗略地说，要研究的构型数量太大，无法进行详尽的分析。由于这个原因，参数空间的大部分区域迄今尚未探索。在这个奖项下，我们将从事一个系统的研究物理参数空间的引力波从紧凑的二元聚结（CBC）使用减少基础的方法。简化基将用于在CBC的某些物理模型中有效地选择参数空间中最相关的区域来求解和分析，compounds表示相应的引力波，并基于这种选择预测新的引力波。简化基建模是基础和应用研究的一个活跃领域，处于许多领域的前沿，从气候研究和天气预报到基因分类和高光谱成像。我们设想，我们在引力物理研究中开发的技术也将在其他领域得到应用。此外，作为我们外展工作的一部分，我们将吸引来自代表性不足群体的学生。特别是，我们将与霍华德大学（全国顶尖的HBCU之一）的学生合作，并在卡多佐和麦考密克等当地西班牙裔高中进行演讲。

Binary systems composed of neutron stars, black holes, or a mixed pair are expected to be some of the most important sources for the upcoming generation of advanced earth-based gravitational wave detectors such as advanced LIGO. Numerous models exist for describing such systems, such as post-Newtonian, phenomenological, Effective One Body ones, and numerical simulations of the full Einstein equations (the field of numerical relativity). Regardless of the model to describe it, the problem suffers from a fairly large dimensionality. Roughly speaking, the number of configurations to study is too large for an exhaustive analysis. For this reason, large regions of the parameter space have been so far unexplored. Under this award, we will engage in a systematic study of the physical parameter space for gravitational waves from compact binary coalescences (CBC) using a Reduced Basis approach. Reduced Basis will be used for efficiently selecting within certain physical models for CBC the most relevant regions in parameter space to solve for and analyze, compactly representing the corresponding gravitational waves, and predicting new ones based on such selection. Reduced Basis modeling is an active area of basic and applied research at the forefront of many fields, from climate studies and weather forecasting to gene classification and hyperspectral imaging. We envision that the techniques we will develop in our gravitational physics research will also find application in other fields. Additionally, as part of our outreach efforts, we will engage students from underrepresented groups. In particular, we will work with students from Howard University (one of the top HBCUs in the country) and give presentations at local Hispanic High Schools such as Cardozo and McCormick.