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

最近先进的LIGO探测到的引力波开启了引力波天文学的新学科。到目前为止，唯一被探测到的光源是合并的黑洞。然而，还有许多其他可能的引力波来源，有些是已知的，有些是未知的。寻找这些来源，以及它们对宇宙结构的贡献，是这门新学科的核心。它们通过LIGO的探测依赖于数据分析工具的发展，这些工具可以从干涉仪的背景中提取引力波信号。对LIGO数据的分析是如此复杂，以至于目前正在开发新的技术来覆盖潜在来源所跨越的大参数空间。该奖项支持如何通过应用新的数值方法加速数据分析管道的研究，这些方法采用了该小组以前从一般数学原理中开发的技术。该奖项支持了一种系统的方法，用于推导双黑洞碰撞发出的波形的封闭形式近似。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，而是会从从头开始模拟完整的爱因斯坦方程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数据分析的重力波形。该项目将是该小组对代理、降阶建模和稀疏表示的研究的延续，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。目标是设计一个系统框架，用于推导来自不同类型源的引力波的封闭形式表达式。该项目的范围将限于使用现有的非旋转黑洞碰撞替代减少基模型来演示概念证明。

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.