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

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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.