This National Science Foundation Project Grant of $229,021 awarded on August 1, 2022 will support research at the University of Texas at Austin to develop mathematical frameworks in optimal transport applications to probability, machine learning, and kinetic theory through July 31, 2025. Under the Mathematical and Physical Sciences program (CFDA 47.049), the investigator will advance understanding of stochastic modeling, artificial intelligence algorithms, and kinetic theory by exploiting...
This $228,693 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research at Michigan State University to develop theoretical tools and efficient numerical methods for solving the optimal transport problem. The research aims to establish existence and characterize long-term behavior of solutions for a class of degenerate-parabolic fully nonlinear partial...
The National Science Foundation awarded a $239,999 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the Georgia Tech Research Corporation from September 15, 2022 to August 31, 2025. The grant funds research to develop mathematical theories and efficient algorithms for multi-marginal optimal transport problems with graphical costs. Specifically, the principal investigator will establish a unified framework for these problems by merging concepts from optimal...
This National Science Foundation Project Grant award of $540,000 provides funding from July 1, 2022 to June 30, 2025 to address new challenges in statistical inference with regularized optimal transport. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049) to Cornell University to explore modern regularization techniques for optimal transport distances and develop a comprehensive statistical theory to facilitate principled inference in high dimensions....
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will provide $160,000 to Cornell University from July 1, 2024 to June 30, 2027 to advance statistical optimal transport theory and its applications. The research project aims to develop new computational and statistical methods for optimal transport, and apply them to various data analysis tasks like clustering, generative modeling, and dimension reduction for...
This National Science Foundation Project Grant award in the amount of $311,024 provides funding from June 15, 2022 through May 31, 2025 to support research advancing the low-regularity theory of certain completely integrable dispersive partial differential equations. The primary goal of the research is to study these systems both for their intrinsic mathematical properties and as tools for understanding the statistical mechanics and dynamics of related physical systems. The awardee, the...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research on the regularity of optimal transport plans and the mathematical understanding of branched microstructures. The $204,069 award to Georgia Tech Research Corporation, which runs from July 2025 to June 2028, will focus on developing a variational approach to studying the regularity of optimal transport in degenerate and singular situations, such as...
This $250,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research in two areas: (1) regularized optimal transport theory and (2) price impact modeling in financial markets. For the first part, the project investigates the mathematical foundations and theoretical guarantees for sparsity in quadratically regularized optimal transport. This builds on prior work on entropically regularized optimal transport....
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $600,000 Project Grant to Carnegie Mellon University (CMU) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports a 3-year research project focused on developing rigorous statistical methods for Optimal Transport, a mathematical technique used to combine data from different scientific domains and mitigate unintended biases in algorithms. The project has three main thrusts: 1)...
This Project Grant award of $113,834 from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program will support research at North Carolina State University (NC State) to develop efficient algorithms for optimal transport in geometric settings. The project aims to advance the theoretical foundations of optimal transport and bridge the gap between theory and practice of optimal transport algorithms. By leveraging combinatorial, geometric and...
This National Science Foundation Project Grant of $315,519 supports research at the University of California, Los Angeles from July 2022 to June 2025 under the Mathematical and Physical Sciences program (CFDA 47.049).
The award funds research investigating challenging problems in optimal transport theory and its applications in fields including partial differential equations, geometry, probability, and machine learning. Key areas of focus include developing the theory to analyze games with large numbers of players, variational problems involving particle systems, and non-commutative optimal transport. The project also initiates inverse optimal transport and inverse mean field game studies. In addition, the grant supports training opportunities for students and researchers involved in interdisciplinary work applying optimal transport concepts.