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

最近先进的LIGO对引力波的探测开启了引力波天文学的新学科。到目前为止，唯一探测到的源是合并的黑洞。然而，引力波还有许多其他可能的来源，一些已知，另一些未知。寻找这些来源，以及它们如何对宇宙结构做出贡献，是这门新学科的核心。通过LIGO探测它们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数据的分析是如此复杂，以至于目前正在开发新的技术，以涵盖潜在来源所跨越的大参数空间。该奖项支持关于如何通过应用新的数值方法来加速数据分析管道的研究，这些新的数值方法使用了该小组以前根据一般数学原理开发的技术。该奖项支持一种系统的方法，用于推导由双黑洞碰撞发出的波形的闭合形式近似。这些封闭形式的表达式不会牺牲保真度或建模精度，也不会执行唯象拟合，而是会从从头算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，只会考虑两个非自转黑洞的情况。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用于数据分析的重力波形。这个项目将是该小组在代理、降阶建模和稀疏表示方面的研究的继续，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。其目标是设计一个系统的框架，用于从不同类型的源推导出引力波的闭合形式表达式。在这个项目中，范围将局限于使用现有的非自旋黑洞碰撞的代理缩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.