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

• 批准号: 2245192
• 负责人: Julianne Chung
• 金额: $ 40.28万
• 依托单位: Emory University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-12-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2245192&HistoricalAwards=false
• 关键词: CAREER; Integrated; Approaches; Fast; Accurate

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.

在各种科学应用中（例如，用于癌症的诊断或地下矿山中的裂纹检测），计算解决方案解决方案的能力至关重要，但是对于合并物理学或数据知识约束的大型非线性问题的计算实时解决方案与当前的反转算法并不可行。此外，由于越来越多地使用了反问题的数值解决方案，用于数据分析并有助于决策，因此这些计算限制在算法中构成了不确定性定量算法中的显着瓶颈（例如，用于估计解决方案方差）。该项目的总体目标是显着降低数值反转的成本，并使统计工具能够帮助科学家做出明智的决定。 这些发展将导致许多重要领域的科学进步。例如，现有与生物医学和采矿工程师的合作将确保拟议的研究可以通过高级护理成像技术进行改进的医学诊断，由于改善地下矿山的地面控制监测而导致的受伤较少，并且可以对地下矿山进行高级信号估算，以实现生理系统的实时分析。此外，PI将继续积极参与鼓励来自历史不足群体的学生的活动。 PI关注的是高中女生的上等小学以及对更大的研究和教学社区（例如K-12教师）的反馈将有助于招募，培训和保留下一代计算科学家的多样化的计算科学家。这项研究将通过在计算问题领域中促进越来越多的逆向方法和更大的框架来促进互为范围的范围，并分析了构建范围和分析范围，并分析了该设计，并分析设计，并分析了分析。将采用一个集成的框架，其中主要的研究推力是（i）开发新颖的正则化方法和实现来处理特定的约束，同时融合了健壮的参数选择方法； （ii）推进技术，以实时计算大型非线性反问题的解决方案（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来实现复杂的非线性系统的关键但无法获得的定量诊断。