Pacific Interdisciplinary Hub on Optimal Transport

University Of Washington, Seattle WA

Investigators

Abstract

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.