Pacific Interdisciplinary Hub on Optimal Transport

该项目涉及最优运输(OT)数学中的合作研究。最初提出的问题是将一组物体从一个位置移动到另一个位置的最有效方式，这个领域在以最佳方式将商品和服务从生产者转移到消费者方面获得了现代意义。该学科随后迅速发展，并在从物理到人工智能的许多科学领域找到了联系和应用。这个项目涉及科学、工程、经济和商业领域的研究人员之间的合作，他们对各自领域的最佳交通运输的作用感兴趣。该小组的目标是回答那些立即适用的基本问题。该小组的战略是(1)快速交流数学知识以解决应用问题，(2)直接受应用启发制定新的数学问题，(3)培养既了解最优运输的强大数学又具有实际应用经验的新一代研究人员。预计学员将成为学术界和产业界新兴就业市场的有力候选人，这些市场看重在应用领域拥有经验的数学家。虽然OT是现代数学的一个重要领域，但它的潜力还没有被广泛地认识到。这个研究小组的目标是回答OT数学中的基本开放问题并探索应用领域，包括构建改进的经济等式度量、OT的熵正则化及其在数据科学中的应用、Wasserstein空间和Wasserstein梯度流的几何及其在大型和/或深度神经网络的采样和分析中的应用，以及多个科学和工程领域的交叉领域的类似问题。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”会改变每个课程，并将结合经济学、机器学习、细胞生物学和梯度流。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.