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

点击翻译按钮获取中文摘要

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.