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

心脏疾病是一种疾病，每年都影响着许多美国人。虽然心电图等技术允许医生假设患者不适的可能原因，但心脏源定位目前不能为医生提供心脏内生物电异常的精确位置，目前的技术也不能为医生提供基于反问题中存在的数值（离散化）误差、建模误差和可变性/不确定性误差的信心措施。本研究涉及计算逆问题中误差和不确定性的量化和控制方法的发展。具体的驱动应用是使计算源定位程序成为诊断心脏生物电场问题的可行工具。这项研究的价值在于它的多学科影响，以及它将计算科学与工程（CS&amp；E）技术扩展到它们设计的原始应用之外。本研究的学术价值在于它对计算逆问题的解决作出了根本性的贡献，并对心脏源定位的生物工程问题作出了实际贡献。在cs&&e的真正精神中，这项研究是特定领域任务和计算科学工具的协同作用。本研究的广泛影响源于其可扩展到更大的计算反问题类别。这项建议的教育目标集中在培训年轻科学家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不连续伽辽金方法，量化和最小化数值建模误差对心电源定位计算的影响；(2)通过探索不确定性量化的多项式混沌方法，量化和最小化源定位过程中的不确定性和可变性的影响。

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.