CAREER: Synergistic Inverse Wave Analysis and Computation

职业：协同逆波分析和计算

• 批准号: 2237534
• 负责人: Yang Yang
• 金额: $ 41.92万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2028-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2237534&HistoricalAwards=false
• 关键词: CAREER; Synergistic; Inverse; Wave; Analysis; CAREER; Synergistic; Inverse; Wave; Analysis

Non-destructive probing techniques utilize waves to probe targets that are not directly observable. They have found broad applications in medical imaging for tumor detection, in seismic imaging for oil prospecting, and in military scenarios for hidden threat detection. The success of modern non-destructive probing techniques relies in an essential way on the mathematical principles that reveal the hidden connection between the observation and the targets. In-depth understanding of such principles will not just reveal the strengths and limitations of the techniques, but also indicate possible directions for future enhancement and improvement. This project aims to promote understanding of the mathematical principles in non-destructive probing techniques from both theoretical and computational perspectives. The theoretical perspective will develop fundamental mathematical tools and methods that are adaptable to resolve challenges in other mathematical branches. The computational perspective will turn the theory into innovative imaging algorithms that empower non-destructive probing techniques to acquire enhanced visualization. Implementation of the project will be integrated with numerous educational activities to involve K-12, undergraduate and graduate students majoring in STEM disciplines, especially those from underrepresented groups with limited educational resources. Students will receive rigorous scientific research training in mathematical and programming skills to prepare them as the next generation of STEM workforce that can continue advancing science and technology in the next few decades.The project aims to investigate fundamental mathematical theory and computational methods for inverse problems for wave equations. This will be achieved by developing the computational boundary control method as well as its underlying mathematical theory. A feature of the approach is the synergy between mathematical analysis and wave-based scientific computing. From the theoretical perspective, the interdisciplinary research will enhance the interplay among PDE analysis, wave physics, geometry, and scientific computing. From the computational perspective, the research will inspire novel computational paradigms that utilize the nature of wave propagation to achieve optimal, theoretically justifiable algorithms for non-destructive probing techniques.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非破坏性探测技术利用波来探测无法直接观察到的靶标。他们在医学成像中发现了广泛的应用，以用于肿瘤检测，地震成像以进行石油勘探以及用于隐藏威胁检测的军事场景。现代非破坏性探测技术的成功依赖于一种基本方式，这些数学原理揭示了观察和目标之间隐藏的联系。对此类原则的深入了解不仅会揭示技术的优势和局限性，而且还指示了未来增强和改进的可能方向。该项目旨在从理论和计算角度促进对非破坏性探测技术中数学原理的理解。理论观点将开发基本的数学工具和方法，这些工具和方法可适应解决其他数学分支中的挑战。计算观点将将理论变成创新的成像算法，这些算法赋予非破坏性探测技术以获取增强的可视化。该项目的实施将与众多教育活动集成，以涉及K-12，本科生和研究生的STEM学科，尤其是来自人为资源有限的人数不足的群体的学生。学生将接受严格的数学和编程技能科学研究培训，以使他们成为下一代STEM劳动力，可以在未来几十年内继续推进科学和技术。该项目旨在调查波动方程的基本数学理论和计算方法。这将通过开发计算边界控制方法及其基本数学理论来实现。该方法的一个特征是数学分析和基于波浪的科学计算之间的协同作用。从理论的角度来看，跨学科研究将增强PDE分析，波浪物理，几何和科学计算之间的相互作用。 From the computational perspective, the research will inspire novel computational paradigms that utilize the nature of wave propagation to achieve optimal, theoretically justifiable algorithms for non-destructive probing techniques.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.