RTG: Mathematical Foundation of Data Science at University of South Carolina

RTG：南卡罗来纳大学数据科学数学基础

• 批准号: 2038080
• 负责人: Linyuan Lu
• 金额: $ 199.66万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2038080&HistoricalAwards=false
• 关键词: RTG; Mathematical; Foundation; Data; Science

This Research Training Group (RTG) project is a joint effort of Mathematics, Statistics, Computer Science and Engineering. It aims to develop a multi-tier Research Training Program at the University of South Carolina (UofSC) designed to prepare the future workforce in a multidisciplinary paradigm of modern data science. The education and training models will leverage knowledge and experience already existing among the faculty and bring in new talent to foster mathematical data science expertise and research portfolios through a vertical integration of post-doctoral research associates, graduate students, undergraduate students, and advanced high school students. A primary focus of this project is to recruit and train U.S. Citizens, females, and underrepresented minority (URM) among undergraduate and graduate students, and postdocs through research led training in Data Science. The research and training infrastructure implemented through this RTG program will not only support the planned majors and master’s degrees, but also provide systemic educational curricula for students and researchers from other areas whose research would benefit from Data Science within UofSC and in the vicinity. The training materials created by this RTG program will also be widely available to other institutions across the country. The RTG project will help build a highly educated workforce for academia, government and industry, in the area of data science, artificial intelligence, and machine learning. This project is a response to emerging demands of modern technology-oriented societies for an innovative workforce with expertise in all areas related to Data Science. Based on a comprehensive view of Data Science, the program aims at providing students and postdocs with the necessary concepts that enable them to form their own research agenda. Our program covers, on the one hand, emerging developments in network science, artificial intelligence, machine learning, and optimization methodologies from computer science and statistical perspectives primarily for the Big-Data regime with applications such as autonomous systems. In addition, problems typically posed in a Small-Data regime can relate these concepts to relevant methodologies, such as Physics Informed Learning, needed to understand mathematical models, usually formulated in terms of Partial Differential Equations (PDEs), so as to understand key techniques for synthesizing models and data in the context of Uncertainty Quantification. Properly interrelating these activities in the broader Data Science landscape, will enable students to successfully tackle new problem areas at later stages of their career and address important challenges in sciences and engineering. The corresponding theoretical training is reinforced by accompanying practical training modules that are able to engage students across all levels as well as young researchers in synergistic activities, even reaching out to local industries. It is a feedback-loop between research and education that distinguishes the project. The educational component is designed with an ultimate goal of developing an innovative research training program to educate future workforce in a structured curriculum that offers a major, a master’s degree and a 4+1 dual degree in Data Science at UofSC. The project facilitates team-teaching by relevant experts and uses direct links to research projects that students will participated in. The built-in vertical and horizontal pedagogical synergies as well as the hierarchical mentoring scheme expose participating students to extensive educational and research experience offered by the program. This project is jointly funded by Computational and Data-enabled Science and Engineering in Mathematical and Statistical Sciences (CDS&E-MSS), the Established Program to Stimulate Competitive Research (EPSCoR), and the Workforce Program in the Mathematical Sciences, among others.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.

这个研究培训小组（RTG）项目是数学，统计，计算机科学和工程的共同努力。它旨在在南卡罗来纳州大学（UofSC）开发一个多层研究培训计划，旨在为现代数据科学的多学科范式中的未来劳动力做好准备。教育和培训模式将利用教师中已有的知识和经验，并通过博士后研究助理，研究生，本科生和高级高中生的垂直整合，引进新的人才，以培养数学数据科学专业知识和研究组合。该项目的主要重点是招募和培训美国公民，女性和本科生和研究生中的代表性不足的少数民族（URM），以及通过数据科学研究主导培训的博士后。通过该RTG计划实施的研究和培训基础设施不仅将支持计划中的专业和硕士学位，还将为其他领域的学生和研究人员提供系统的教育课程，这些学生和研究人员的研究将受益于UofSC及其附近的数据科学。由该RTG计划创建的培训材料也将广泛提供给全国各地的其他机构。RTG项目将帮助学术界、政府和工业界在数据科学、人工智能和机器学习领域建立一支受过高等教育的劳动力队伍。该项目是对现代技术导向型社会对具有数据科学相关所有领域专业知识的创新劳动力的新兴需求的回应。基于数据科学的全面观点，该计划旨在为学生和博士后提供必要的概念，使他们能够形成自己的研究议程。一方面，我们的计划涵盖了网络科学，人工智能，机器学习和优化方法的新兴发展，从计算机科学和统计学的角度来看，主要用于大数据制度，如自治系统的应用。此外，通常在小数据制度中提出的问题可以将这些概念与相关方法联系起来，例如物理学知情学习，需要理解数学模型，通常用偏微分方程（PDE）来表示，以便理解在不确定性量化的背景下合成模型和数据的关键技术。在更广泛的数据科学领域中将这些活动适当地相互关联，将使学生能够在职业生涯的后期成功地解决新的问题领域，并解决科学和工程领域的重要挑战。相应的理论培训通过附带的实践培训模块得到加强，这些模块能够让各级学生以及年轻的研究人员参与协同活动，甚至深入到当地产业。这是研究和教育之间的反馈回路，使该项目与众不同。教育部分的设计最终目标是开发一个创新的研究培训计划，以教育未来的劳动力在结构化的课程，提供一个主要的，硕士学位和4+1双学位的数据科学在UofSC。该项目促进了相关专家的团队教学，并与学生将参与的研究项目直接联系。内置的纵向和横向教学协同作用以及分层指导计划使参与学生获得该计划提供的广泛教育和研究经验。该项目由数学和统计科学中的计算和数据支持的科学与工程（CDS E-MSS）、激励竞争性研究的既定计划（EPSCoR）和数学科学中的劳动力计划等共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

FELARE: Fair Scheduling of Machine Learning Tasks on Heterogeneous Edge Systems

• DOI: 10.1109/cloud55607.2022.00069
• 发表时间: 2022-05
• 期刊: 2022 IEEE 15th International Conference on Cloud Computing (CLOUD)
• 作者: Ali Mokhtari;Pooyan Jamshidi;M. Salehi

Computational mean-field games on manifolds

• DOI: 10.1016/j.jcp.2023.112070
• 发表时间: 2022-06
• 期刊: J. Comput. Phys.
• 作者: Jiajia Yu;Rongjie Lai;Wuchen Li;S. Osher

Concentration inequalities in spaces of random configurations with positive Ricci curvatures

具有正里奇曲率的随机配置空间中的浓度不等式

• 发表时间: 2022
• 期刊: Pure and applied mathematics quarterly
• 影响因子: 0.7
• 作者: Lu, Linyuan;Wang, Zhiyu
• 通讯作者: Wang, Zhiyu

Improved Lower Bounds on the Extrema of Eigenvalues of Graphs

图特征值极值的改进下界

• DOI: 10.1007/s00373-023-02678-0
• 发表时间: 2023
• 期刊: Graphs and Combinatorics
• 影响因子: 0.7
• 作者: Linz, William

Controlling conservation laws I: Entropy–entropy flux

控制守恒定律 I：熵 — 熵通量

• DOI: 10.1016/j.jcp.2023.112019
• 发表时间: 2023
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Li, Wuchen;Liu, Siting;Osher, Stanley
• 通讯作者: Osher, Stanley