CAREER: Mathematical Modeling from Data to Insights and Beyond

职业：从数据到见解及其他的数学建模

• 批准号: 2414705
• 负责人: Yifei Lou
• 金额: $ 40.02万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-15 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2414705&HistoricalAwards=false
• 关键词: CAREER; Mathematical; Modeling; Data; Insights

This project will develop both analytical and computational tools for data-driven applications. In particular, analytical tools will hold great promise to provide theoretical guidance on how to acquire data more efficiently than current practices. To retrieve useful information from data, numerical methods will be investigated with emphasis on guaranteed convergence and algorithmic acceleration. Thanks to close interactions with collaborators in data science and information technology, the investigator will ensure the practicability of the proposed research, leading to a real impact. The investigator will also devote herself to various outreach activities in the field of data science. For example, she will initiate a local network of students, faculty members, and domain experts to develop close ties between mathematics and industry as well as to broaden career opportunities for mathematics students. This initiative will have a positive impact on the entire mathematical sciences community. In addition, she will advocate for the integration of mathematical modeling into K-16 education by collaborating with The University of Texas at Dallas Diversity Scholarship Program to reach out to mathematics/sciences teachers.This project addresses important issues in extracting insights from data and training the next generation in the "big data" era. The research focuses on signal/image recovery from a limited number of measurements, in which "limited" refers to the fact that the amount of data that can be taken or transmitted is limited by technical or economic constraints. When data is insufficient, one often requires additional information from the application domain to build a mathematical model, followed by numerical methods. Questions to be explored in this project include: (1) how difficult is the process of extracting insights from data? (2) how should reasonable assumptions be taken into account to build a mathematical model? (3) how should an efficient algorithm be designed to find a model solution? More importantly, a feedback loop from insights to data will be introduced, i.e., (4) how to improve upon data acquisition so that information becomes easier to retrieve? As these questions mimic the standard procedure in mathematical modeling, the proposed research provides a plethora of illustrative examples to enrich the education of mathematical modeling. In fact, one of this CAREER award's educational objectives is to advocate the integration of mathematical modeling into K-16 education so that students will develop problem-solving skills in early ages. In addition, the proposed research requires close interactions with domain experts in business, industry, and government (BIG), where real-world problems come from. This requirement helps to fulfill another educational objective, that is, to promote BIG employment by providing adequate training for students in successful approaches to BIG problems together with BIG workforce skills.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.

该项目将为数据驱动的应用程序开发分析和计算工具。特别是，分析工具将对如何比当前实践更有效地获得有关如何更有效地获取数据的理论指导。为了从数据中检索有用的信息，将研究数值方法，重点是保证收敛和算法加速度。由于与数据科学和信息技术的合作者进行了密切的互动，研究人员将确保拟议研究的实用性，从而产生真正的影响。研究人员还将专门研究数据科学领域的各种外展活动。例如，她将启动当地的学生，教职员工和领域专家网络，以在数学和行业之间建立紧密联系，并扩大数学学生的职业机会。该计划将对整个数学科学社区产生积极影响。此外，她将通过与德克萨斯大学达拉斯大学多样性奖学金计划合作将数学建模集成到K-16教育中，以与数学/科学教师接触。该项目解决了从数据中提取洞察力的重要问题，并从数据中提取洞察力，并培训了“大数据”时代的下一代。该研究的重点是从有限数量的测量值中恢复信号/图像，其中“有限”指的是，可以获取或传输的数据量受到技术或经济限制的限制。当数据不足时，通常需要从应用程序域中的其他信息来构建数学模型，然后使用数值方法。该项目中要探讨的问题包括：（1）从数据中提取见解的过程有多困难？ （2）如何考虑合理的假设来构建数学模型？ （3）如何设计有效的算法来找到模型解决方案？更重要的是，将引入从洞察力到数据的反馈循环，即（4）如何改进数据获取以使信息变得更容易检索？由于这些问题模仿了数学建模中的标准程序，因此拟议的研究提供了许多说明性示例，以丰富数学建模的教育。实际上，该职业奖的一个教育目标之一是主张将数学建模整合到K-16教育中，以便学生在早期发展解决问题的技能。此外，拟议的研究需要与现实世界中问题来自的商业，行业和政府（BIG）领域的领域专家进行密切的互动。这项要求有助于实现另一个教育目标，即，通过为学生提供足够的培训，以成功地解决大问题，并与大型劳动力技能一起提供足够的培训。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响审查标准来通过评估来获得支持的。