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CAREER: Integrated Approaches for Fast and Accurate Large-Scale Inversion

职业：快速准确的大规模反演的综合方法

基本信息

批准号：
1654175
负责人：
Julianne Chung
金额：
$ 40.28万
依托单位：
Virginia Polytechnic Institute and State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2023-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1654175&HistoricalAwards=false
关键词：
CAREER Integrated Approaches Fast Accurate

项目摘要

The ability to compute solutions to inverse problems is essential in various scientific applications (e.g., for cancer diagnosis or for crack detection in underground mines), but computing real-time solutions to large nonlinear problems that incorporate physics- or data-informed constraints is not feasible with current inversion algorithms. Moreover, as numerical solutions to inverse problems are increasingly being used for data analysis and to aid in decision-making, these computational limitations pose significant bottlenecks in algorithms for uncertainty quantification (e.g., for estimating solution variances). The overarching goal of this project is to significantly reduce the costs of numerical inversion and to enable statistical tools to aid scientists in making informed decisions. These developments will lead to scientific advancement in many important fields. For example, existing collaborations with biomedical and mining engineers will ensure that the proposed research can result in improved medical diagnosis via advanced point-of-care imaging technologies, fewer injuries due to improved ground control monitoring of underground mines, and advanced signal estimation for real-time analysis of physiological systems. Moreover, the PI will continue to actively engage in activities that encourage students from historically under-represented groups. The PI's focus on upper elementary to high school girls and on outreach that will feed back into the greater research and teaching communities (e.g., K-12 teachers) will contribute to the recruitment, training, and retention of a diverse next generation of computational scientists.This research will advance knowledge in the field of computational inverse problems by developing faster methodologies and more robust frameworks for the design, computation, and analysis of solutions to inverse problems. An integrated framework will be adopted, where the main research thrusts are (i) to develop novel regularization methods and implementations to handle application-specific constraints, while simultaneously incorporating robust parameter selection methods; (ii) to advance technologies for real-time computation of solutions to large, nonlinear inverse problems (e.g., by integrating stochastic methods and update approaches); and (iii) to enable critical, yet previously unobtainable, quantitative diagnostics for complex, nonlinear systems by developing efficient error estimation methods.

计算反问题的解的能力在各种科学应用中是必不可少的（例如，癌症诊断或地下矿山的裂缝检测），但是计算包含物理或数据信息约束的大型非线性问题的实时解在当前的反演算法中是不可行的。此外，随着反问题的数值解越来越多地用于数据分析和帮助决策，这些计算限制对不确定性量化算法（例如，估计解方差）构成了重大瓶颈。该项目的首要目标是显著降低数值反演的成本，并使统计工具能够帮助科学家做出明智的决策。这些发展将导致许多重要领域的科学进步。例如，与生物医学和采矿工程师的现有合作将确保拟议的研究能够通过先进的即时成像技术改善医疗诊断，通过改进地下矿山的地面控制监测减少伤害，以及用于生理系统实时分析的先进信号估计。此外，PI将继续积极参与鼓励来自历史上代表性不足的群体的学生的活动。PI的重点是小学高年级到高中女生，并将其推广到更大的研究和教学社区（例如，K-12教师），这将有助于招聘、培训和留住多样化的下一代计算科学家。这项研究将通过开发更快的方法和更强大的框架来设计、计算和分析反问题的解决方案，从而推进计算反问题领域的知识。将采用一个集成框架，其中主要研究重点是(i)开发新的正则化方法和实现来处理特定应用的约束，同时结合鲁棒参数选择方法；（ii）推进大型非线性逆问题解的实时计算技术（例如，通过整合随机方法和更新方法）；（iii）通过开发有效的误差估计方法，对复杂的非线性系统进行关键但以前无法获得的定量诊断。