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，用于以可靠的精度估算重力波模拟中计算的波形的误差，以支持NSF资助的激光干涉仪重力仪表仪（LIGO）。 该项目汇集了一组应用和计算数学家团队，该团队在构建部分微分方程解决方案的错误估计和物理学家方面具有专业知识，并具有在爱因斯坦方程和重力波数据分析的数值解决方案方面具有专业知识。 主要的技术目标是开发和分析重力物理社区可以使用的新数学和计算方法，以计算对爱因斯坦方程数值溶液的误差以及由它们确定的重力波形的严格且可靠地准确的估计。 特别是，本研究探讨了以下问题：（1）使用伴随灵敏度技术及其相关的数值实施的错误量化和后验分析；（2）由目标误差控制及其相关的理论融合分析驱动的自适应算法； （3）协方差对称性和相关的几何结构在误差分析和数值方法的构建中的作用。作为A后验分析的一部分，项目团队将开发爱因斯坦方程的伴随运算符和二元性的基本理论。这将为未来研究使用LIGO数据的敏感性分析，数据同化和不确定性定量的基础。应该强调的是，拟议的研究的主要目的是离散化的中立，因此在存在的数值相对性代码的范围内具有广泛的适用性。NSF支持的激光干涉仪重力引力观测值（Ligo）仅在高度准确的绘制范围内才能成功地进行绘制，以便在高度准确的范围内使用数据分析，该过程既可以使用数据，又可以分析数据，该分析能够分析，部分，部分。任何检测到的信号的属性。 重力波的最强来源预计是重，致密的恒星或黑洞之间的碰撞，只能使用复杂的数值模拟来准确对其进行建模，以计算预期的引力波形。 需要这样的波形来构建允许检测噪声检测器中弱重力波信号的过滤器，并且还需要进行此类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准确性很高。 但是，数值相对性社区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。 如果数值相对性社区当前使用的定性准确性措施过于乐观，那么该项目开发的严格新方法可能会使Ligo的成功与失败之间有所不同。 如果当前的数值波形实际上足够准确，则该项目开发的方法可以提高以指定精度水平确定波形的计算效率，从而降低产生它们的成本。