FRG: Collaborative Research: Error Quantification and Control for Gravitational Waveform Simulation

FRG：协作研究：重力波形仿真的误差量化和控制

• 批准号: 1065972
• 负责人: Michael Holst
• 金额: $ 45.49万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-15 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1065972&HistoricalAwards=false
• 关键词: FRG; Collaborative; Research; Error; Quantification

The purpose of this project is to develop practical rigorous methods for estimating the error in computed waveforms from gravitational wave simulation with reliable accuracy, in support of the NSF-funded Laser Interferometer Gravitational Observatory (LIGO). The project brings together a team of applied and computational mathematicians with expertise in constructing error estimates for solutions of partial differential equations and physicists with expertise in numerical solutions of the Einstein equation and gravitational wave data analysis. The primary technical goal is to develop and analyze new mathematical and computational methods that can be used by the gravitational physics community to compute rigorous and reliably accurate estimates for the errors of numerical solutions of the Einstein equations and the gravitational waveforms that are determined from them. In particular, this research explores the following issues:(1) Error quantification and a posteriori analysis using adjoint sensitivity techniques, and their associated numerical implementation;(2) Adaptive algorithms that are driven by goal-oriented error control, and their associated theoretical convergence analysis; and(3) The role of covariance symmetry and associated geometric structures in error analysis and the construction of numerical methods.As part of the a posteriori analysis, the project team will develop the basic theory of adjoint operators and duality for the Einstein equations. This will provide the foundation for future investigations into sensitivity analysis, data assimilation and uncertainty quantification for using LIGO data. It should be emphasized that the main thrusts of the proposed research are discretization-neutral, and therefore have broad applicability to the breadth of numerical relativity codes in existence.The NSF-supported Laser Interferometer Gravitational Observatory (LIGO) can be successful only if highly accurate gravitational waveform models are available for use as part of the data analysis process, both for detecting gravitational waves and also for measuring the physical properties of any detected signals. The strongest sources of gravitational waves are expected to be collisions between heavy, dense stars or black holes, which can only be modeled accurately using complex numerical simulations to calculate the anticipated gravitational waveforms. Such waveforms are needed to construct the filters that allow detection of the weak gravitational-wave signals in the noisy detector, and such waveforms are also needed to measure the physical properties of the sources of any detected signals. The waveform accuracy needed to accomplish the required data analysis tasks is quite high. However, the numerical relativity community has yet to develop the analytic and computational tools needed to evaluate rigorously the accuracy of the numerical waveform models. If the qualitative accuracy measures currently used by the numerical relativity community are too optimistic, the rigorous new methods developed by this project could make the difference between success and failure of LIGO. If the current numerical waveforms are in fact accurate enough, the methods developed by this project could improve the computational efficiency of determining waveforms with a specified accuracy level, and thus reduce the cost of producing them.

该项目的目的是开发实用的严格方法，以可靠的精度估计引力波模拟计算波形的误差，以支持 NSF 资助的激光干涉仪重力观测站 (LIGO)。 该项目汇集了一支由具有构建偏微分方程解误差估计专业知识的应用和计算数学家和具有爱因斯坦方程数值解和引力波数据分析专业知识的物理学家组成的团队。 主要技术目标是开发和分析新的数学和计算方法，引力物理学界可以使用这些方法对爱因斯坦方程的数值解和由此确定的引力波形的误差进行严格且可靠的准确估计。 具体来说，本研究探讨了以下问题：（1）使用伴随灵敏度技术的误差量化和后验分析及其相关的数值实现；（2）由目标导向误差控制驱动的自适应算法及其相关的理论收敛性分析; (3)协方差对称性和相关几何结构在误差分析和数值方法构建中的作用。作为后验分析的一部分，项目团队将开发爱因斯坦方程的伴随算子和对偶性的基本理论。这将为未来使用 LIGO 数据进行敏感性分析、数据同化和不确定性量化的研究奠定基础。应该强调的是，拟议研究的主旨是离散化中性的，因此对现有的数值相对论代码具有广泛的适用性。 NSF 支持的激光干涉仪重力观测站（LIGO）只有在高精度的情况下才能成功引力波形模型可用作数据分析过程的一部分，既可用于检测引力波，也可用于测量任何检测到的信号的物理特性。 最强的引力波源预计是重而密的恒星或黑洞之间的碰撞，只能使用复杂的数值模拟来精确建模，以计算预期的引力波形。 需要这样的波形来构造滤波器，以允许在有噪声的探测器中检测微弱的引力波信号，并且还需要这样的波形来测量任何检测到的信号源的物理特性。 完成所需的数据分析任务所需的波形精度相当高。 然而，数值相对论界尚未开发出严格评估数值波形模型准确性所需的分析和计算工具。 如果数值相对论界目前使用的定性精度测量过于乐观，那么该项目开发的严格的新方法可能会决定 LIGO 的成功与失败。 如果当前的数值波形实际上足够准确，那么该项目开发的方法可以提高确定具有指定精度水平的波形的计算效率，从而降低生成波形的成本。