CAREER: Quantifying and Controlling Error and Uncertainty in Computational Inverse Problems

职业：量化和控制计算逆问题中的误差和不确定性

• 批准号: 0347791
• 负责人: Robert Kirby
• 金额: --
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0347791&HistoricalAwards=false
• 关键词: CAREER; Quantifying; Controlling; Error; Uncertainty

ABSTRACT0347791Robert M. KirbyUniversity of UtahHeart disorders are a malady, which affect many Americans each year. Although techniques such as electrocardiography allow physicians to postulate as the probable cause of patient discomfort, cardiac source localization cannot currently provide the physician with the precise location within the heart of a bioelectric abnormality, nor can current techniques provide the physician with confidence measures based upon the numerical (discretization) errors, modeling errors and variability/uncertainty errors which exist in the inverse problem. This research involves the development of methods for quantifying and controlling error and uncertainty in computational inverse problems. The specific driving application is to make the computational source localization procedure a viable tool for diagnosing cardiac bioelectric field problems. This research is valuable for both its multi-disciplinary influence and its expansion of computational science and engineering (CS&E) techniques beyond the original applications for which they were designed. The academic merit of this research is its fundamental contribution to the solution of computational inverse problems and its practical contribution to the bioengineering problem of cardiac source localization. In the true spirit of CS&E, this research is the synergy of a domain specific task and computational science tools. The broader impact of this research results from its extendibility to a much larger class of computational inverse problems. The educational objectives of this proposal are focused on training young scientists to properly view simulation science as a tool in the validation of and extension of scientific inquiry. Specifically, this research is partitioned into two aims: (1) to quantify and minimize the effects of numerical modeling errors in the ECG source localization computation through the judicious use of high-order methods and the discontinuous Galerkin method; and (2) to quantify and minimize the effects of uncertainty and variability in the source localization process through the exploration of the polynomial chaos methodology for uncertainty quantification.

犹他州大学罗伯特·M·柯比心脏病是一种疾病，每年影响许多美国人。尽管诸如心电图学之类的技术允许医生假定为患者不适的可能原因，但是心源定位目前不能向医生提供生物电异常在心脏内的准确位置，当前的技术也不能基于逆问题中存在的数值(离散化)误差、建模误差和可变性/不确定性误差向医生提供置信度测量。这项研究涉及定量和控制计算反问题中的误差和不确定性的方法的发展。具体的驱动应用是使计算源定位过程成为诊断心脏生物电场问题的可行工具。这项研究既有多学科的影响，也有扩展计算科学和工程(CS&Amp；E)技术的价值，超出了它们最初设计的应用范围。这项研究的学术价值在于它对计算反问题的解决做出了基础性贡献，并对心脏来源定位的生物工程问题做出了实际贡献。本着CS&Ame的真正精神，这项研究是特定领域任务和计算科学工具的协同。这项研究的更广泛的影响是因为它可以扩展到更大类别的计算反问题。这项提议的教育目标侧重于培训青年科学家正确地将模拟科学视为验证和推广科学探究的工具。具体地说，本研究分为两个目标：(1)通过合理使用高阶方法和不连续Galerkin方法来量化和最小化心电源定位计算中数值建模误差的影响；(2)通过探索用于不确定性量化的多项式混沌方法来量化和最小化源定位过程中的不确定性和变异性的影响。