RTG: Applied Mathematics and Statistics for Data-Driven Discovery

RTG：数据驱动发现的应用数学和统计学

• 批准号: 1937229
• 负责人: Kevin Lin
• 金额: $ 200万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1937229&HistoricalAwards=false
• 关键词: RTG; Applied; Mathematics; Statistics; Data

The simultaneous availability of large datasets, high performance computing, and modern machine learning algorithms holds great promise to enable scientists and engineers to rapidly discover hidden patterns in data, and to utilize these patterns to understand the natural world in order to solve pressing practical problems facing society. Realizing this promise requires addressing many mathematical and computational challenges: in framing scientific and technological problems for solution by data-driven approaches, in interpreting and analyzing data, and in designing efficient and reliable algorithms. There is an urgent need for mathematical scientists who are equally adept at wielding modern applied and computational mathematics on the one hand, and the tools of data-driven modeling, statistical inference, and scientific computing on the other. Furthermore, as interdisciplinary research and development become more common in industry, academia, and government, it is imperative that such mathematical scientists be generalists, able to communicate and work with specialists from diverse fields. This Research Training Group (RTG) addresses this need by increasing the number of mathematical scientists capable of working effectively at the interface of applied mathematics/statistics and modern data science. By focusing on specific applications requiring both mathematical innovation and data-driven modeling and by forming teams of mathematical scientists and domain experts, the RTG will enable trainees to address new challenges in innovative ways using their mastery of relevant mathematics, statistics and data science, and domain knowledge. Recognizing the challenges of advanced studies in STEM fields, the RTG will promote close, small-group mentoring at all levels. The expected outcome is mathematical scientists adept at working at disciplinary boundaries and intellectually equipped to tackle a wide range of scientific and technological challenges. It is expected that some of the trainees will continue in academia, where the proposed training activities can be improved and propagated; others will work in industry and government, applying their knowledge and skills to solve problems of practical significance.The RTG will support research on applied mathematics and data-driven modeling at the University of Arizona (UA), which is home to a large and vibrant mathematical science community. It is organized around a number of application-centered Working Groups, with foci ranging from analysis of gene regulation data to the modeling and forecasting of power grids. Each research project will impact both fundamental methodology and practical applications. The Working Groups are structured to enable vertically-integrated mentoring of RTG trainees at all levels -- undergraduate, graduate, and postdoctoral, and to enable trainees to work closely with Mathematics faculty and domain experts. Additional training activities include courses on foundational topics, e.g., optimization, machine learning, Monte Carlo methods, as well as practical skills such as software carpentry. By providing research training at the interface between the traditional domains of applied mathematics and the cutting-edge field of data-driven modeling, the RTG will both advance scientific knowledge and increase the number of US citizens and nationals with much-needed scientific and technological expertise.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.

大型数据集、高性能计算和现代机器学习算法的同时可用性，使科学家和工程师能够快速发现数据中隐藏的模式，并利用这些模式来理解自然世界，以解决社会面临的紧迫实际问题。实现这一承诺需要解决许多数学和计算挑战：通过数据驱动的方法来解决科学和技术问题，解释和分析数据，以及设计高效可靠的算法。迫切需要数学科学家，他们一方面同样擅长运用现代应用和计算数学，另一方面也擅长数据驱动建模，统计推断和科学计算的工具。此外，随着跨学科研究和开发在工业界、学术界和政府中变得越来越普遍，这些数学科学家必须是通才，能够与来自不同领域的专家进行沟通和合作。该研究培训小组（RTG）通过增加能够在应用数学/统计学和现代数据科学的界面上有效工作的数学科学家的数量来满足这一需求。通过专注于需要数学创新和数据驱动建模的特定应用，并通过组建数学科学家和领域专家团队，RTG将使学员能够利用他们对相关数学，统计和数据科学以及领域知识的掌握，以创新的方式应对新的挑战。认识到在STEM领域的高级研究的挑战，RTG将促进在各级密切，小组辅导。预期的结果是数学科学家善于在学科界限上工作，并有能力应对广泛的科学和技术挑战。预计一些学员将继续在学术界工作，以改进和推广拟议的培训活动;其他人将在工业界和政府工作，应用他们的知识和技能解决具有实际意义的问题。RTG将支持亚利桑那大学（UA）的应用数学和数据驱动建模研究，该大学是一个庞大而充满活力的数学科学社区的所在地。它是围绕一些以应用为中心的工作组组织的，重点从基因调控数据的分析到电网的建模和预测。每个研究项目都将影响基本方法和实际应用。工作组的结构，使RTG学员在所有级别-本科生，研究生和博士后的垂直整合辅导，并使学员与数学教师和领域专家密切合作。其他培训活动包括关于基本专题的课程，例如，优化，机器学习，蒙特卡罗方法，以及软件木工等实用技能。通过在应用数学的传统领域和数据驱动建模的前沿领域之间的接口提供研究培训，RTG将促进科学知识的发展，增加美国公民和国民的数量，该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的评估被认为值得支持。影响审查标准。

项目成果

Modeling illegal logging in Brazil

巴西非法采伐建模

• DOI: 10.1007/s40687-021-00263-6
• 发表时间: 2021
• 期刊: Research in the Mathematical Sciences
• 影响因子: 1.2
• 作者: Chen, Bohan;Peng, Kaiyan;Parkinson, Christian;Bertozzi, Andrea L.;Slough, Tara Lyn;Urpelainen, Johannes
• 通讯作者: Urpelainen, Johannes

A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations

• DOI: 10.1007/s10915-021-01531-x
• 发表时间: 2020-05
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: C. Parkinson