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

摘要0347791罗伯特M.心脏病是一种疾病，每年影响许多美国人。 尽管诸如心电图之类的技术允许医生假设患者不适的可能原因，但是心脏源定位目前不能为医生提供生物电异常在心脏内的精确位置，当前的技术也不能为医生提供基于逆问题中存在的数值（离散化）误差、建模误差和可变性/不确定性误差的置信度测量。 这项研究涉及的方法，量化和控制计算反问题中的误差和不确定性的发展。 具体的驱动应用程序是使计算源定位程序诊断心脏生物电场问题的可行工具。 这项研究是有价值的，其多学科的影响和扩展的计算科学与工程（CS E）技术超出了原来的应用程序，他们的设计。 本研究的学术价值在于其对计算逆问题的解决的基础性贡献和对心脏源定位的生物工程问题的实际贡献。在CS E的真正精神，这项研究是特定领域的任务和计算科学工具的协同作用。更广泛的影响，这项研究的结果，从它的可扩展性，更大的一类计算反问题。 该建议的教育目标侧重于培训年轻科学家，使其正确地将模拟科学视为验证和扩展科学探究的工具。 具体而言，本研究分为两个目标：（1）通过合理使用高阶方法和间断Galerkin方法，量化和最小化数值建模误差在ECG源定位计算中的影响;以及（2）通过探索不确定性的多项式混沌方法，量化和最小化源定位过程中的不确定性和可变性的影响量化

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.