Reduced Basis, Symbolic Regression, and Closed Form Expressions for Gravitational Waves

最近，Advanced LIGO对引力波的探测开创了引力波天文学的新学科。 迄今为止，唯一被探测到的来源是合并黑洞。 然而，还有许多其他可能的引力波源，一些已知，另一些未知。 寻找这些来源，以及它们如何对宇宙的结构做出贡献，是这门新学科的核心。 通过LIGO的探测依赖于数据分析工具的开发，这些工具允许从干涉仪背景中提取引力波信号。 LIGO数据的分析是如此的复杂，以至于目前正在开发新的技术来覆盖潜在源所跨越的大参数空间。该奖项支持通过应用新的数值方法来加速数据分析流程的研究，这些方法采用了该小组以前从一般数学原理开发的技术。该奖项支持导出二元黑洞碰撞发射波形的封闭形式近似的系统方法。这些封闭形式的表达式不会牺牲保真度或建模精度，不会执行现象学拟合，而是会从完整爱因斯坦方程的从头计算模拟中找到封闭形式的表达式。虽然这种方法是通用的，但在这个项目中，只有两个非旋转黑洞的情况才会被考虑。该项目的目标是为LIGO项目提供一种非常快速的方法来评估数据分析的重力波形。该项目将是该小组在替代和降阶建模和稀疏表示方面研究的延续，并将其应用于引力波。它将通过遗传编程增加符号回归的额外推力。我们的目标是设计一个系统的框架来推导来自不同类型源的引力波的封闭形式的表达式。在这个项目中，范围将限于使用现有的替代简化基础模型来证明非旋转黑洞碰撞的概念。

The recent detection of gravitational waves by Advanced LIGO has ushered in the new discipline of gravitational wave astronomy. To date the only sources that have been detected are merging black holes. However, there are many other possible sources for gravitational waves, some known and others unknown. The search for these sources, and how they contribute to the structure of the cosmos, lies at the heart of this new discipline. Their detection through LIGO relies on the development of data analysis tools that allow the extraction of the gravitational wave signal from the interferometer background. The analysis of LIGO data is of such complexity that new techniques are currently being developed to cover the large parameter space spanned by potential sources. This award supports research on how to accelerate data analysis pipelines through application of new numerical methods that employ techniques previously developed by the group from general mathematical principles.This award supports a systematic approach for deriving closed form approximations of waveforms emitted by binary black hole collisions. These closed form expressions will not sacrifice fidelity or modeling accuracy, will not perform phenomenological fits, but instead will find closed form expressions from ab-initio simulations of the full Einstein equations. Though the approach will be generic, during this project only the case of two non-spinning black holes will be considered. The goal of this project is to provide the LIGO project with a very fast way of evaluating gravitational waveforms for data analysis. This project will be a continuation of the group's research on surrogate and reduced order modeling and sparse representations, with applications to gravitational waves. It will add the additional thrust of symbolic regression through genetic programming. The goal is to design a systematic framework for deriving closed form expressions for gravitational waves from different types of sources. The scope will be limited in this project to demonstrating a proof of concept using existing surrogate reduced basis models for non-spinning black hole collisions.