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

Advanced LIGO 最近对引力波的探测开创了引力波天文学的新学科。 迄今为止，已检测到的唯一来源是合并黑洞。 然而，引力波还有许多其他可能的来源，有些是已知的，有些是未知的。 寻找这些来源，以及它们如何对宇宙结构做出贡献，是这一新学科的核心。 它们通过 LIGO 的探测依赖于数据分析工具的开发，该工具允许从干涉仪背景中提取引力波信号。 LIGO 数据的分析非常复杂，目前正在开发新技术来覆盖潜在源跨越的大参数空间。该奖项支持研究如何通过应用新的数值方法来加速数据分析流程，这些方法采用了该小组之前根据一般数学原理开发的技术。该奖项支持一种系统方法，用于推导二元黑洞碰撞发出的波形的封闭形式近似值。这些闭合形式表达式不会牺牲保真度或建模准确性，不会执行唯象拟合，而是从完整爱因斯坦方程的从头开始模拟中找到闭合形式表达式。尽管该方法是通用的，但在该项目中仅考虑两个非旋转黑洞的情况。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引力波形以进行数据分析。该项目将是该小组对替代和降阶建模以及稀疏表示研究的延续，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动力。目标是设计一个系统框架，用于导出不同类型源的引力波的封闭形式表达式。该项目的范围仅限于使用现有的非旋转黑洞碰撞替代简化基础模型来演示概念验证。

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.