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Pacific Interdisciplinary Hub on Optimal Transport

太平洋最佳交通跨学科中心

基本信息

批准号：
2133244
负责人：
Soumik Pal
金额：
$ 22.2万
依托单位：
University of Washington
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-05-01 至 2025-04-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2133244&HistoricalAwards=false
关键词：
Pacific Interdisciplinary Hub Optimal Transport

项目摘要

This project concerns collaborative research in the mathematics of optimal transport (OT). Originally posed as a question about the most efficient way to move a set of objects from one location to another, this area achieved modern significance in connection with optimally "transporting" goods and services from producers to consumers. The subject has subsequently developed rapidly and found connections to and applications in a host of scientific areas, from physics to artificial intelligence. This project involves collaborative work among researchers in the sciences, engineering, economics, and business who have interest in the role of optimal transport in their respective fields. The group aims to answer fundamental questions that have immediate application. The group's strategy is to (1) quickly exchange mathematical knowledge to solve applied problems, (2) formulate new mathematical questions inspired directly by applications, and (3) train a new generation of researchers who both understand the powerful mathematics of optimal transport and are experienced in its practical applications. Student trainees are expected to be strong candidates in emerging job markets in both academia and industry that value mathematicians with experience in application areas. Although OT is a major area in modern mathematics, its potential is still not widely realized. This research group aims to answer fundamental open questions in the mathematics of OT as well as to explore areas of application, including constructing improved metrics of economic equality, entropic regularization of OT and applications to data science, the geometry of Wasserstein space and Wasserstein gradient flows with applications to sampling and analysis of large and/or deep neural networks, and similar questions at the intersection of multiple areas of science and engineering. The project includes multi-disciplinary training of students in theory, application, and computation, as well as development of a sequence of "OT+X" online courses, where the subject "X" changes each offering and will incorporate economics, machine learning, cell biology, and gradient flows.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.

该项目涉及最佳运输（OT）数学的合作研究。这个领域最初是作为一个关于如何最有效地将一组物品从一个地点移动到另一个地点的问题提出的，但在将商品和服务从生产者最佳地“运输”到消费者方面，它取得了现代意义。该学科随后迅速发展，并在从物理学到人工智能的许多科学领域中找到了联系和应用。该项目涉及科学，工程，经济和商业研究人员之间的合作，他们对各自领域的最佳运输的作用感兴趣。该小组旨在回答具有直接应用的基本问题。该小组的战略是（1）快速交流数学知识以解决应用问题，（2）制定直接受应用启发的新数学问题，（3）培养新一代研究人员，他们既了解最佳运输的强大数学，又在其实际应用中有经验。学生学员预计将成为学术界和工业界新兴就业市场的有力候选人，这些市场重视具有应用领域经验的数学家。虽然OT是现代数学中的一个重要领域，但它的潜力仍然没有得到广泛的认识。该研究小组旨在回答OT数学中的基本开放问题，并探索应用领域，包括构建经济平等的改进指标，OT的熵正则化和数据科学的应用，Wasserstein空间和Wasserstein梯度流的几何形状以及对大型和/或深度神经网络的采样和分析，以及科学和工程多个领域交叉点的类似问题。该项目包括对学生进行理论、应用和计算方面的多学科培训，以及开发一系列“OT+X”在线课程，其中主题“X”改变了每个课程，并将纳入经济学、机器学习、细胞生物学、该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准。