Project Grant 2606084
- The National Science Foundation awarded the University of North Carolina at Chapel Hill $380,000 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) for collaborative research on machine learning on stratified matrix manifolds under group actions. The project develops novel methodologies integrating topology, geometry, and machine learning to enable data-driven discovery across scientific domains. Work is organized into three thrusts: establishing mathematical and...
- The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill $174,999 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop the Binary Expansion Group Intersection Network (BEGIN), a statistical framework for learning from data represented at the binary digit level. The project will construct graphical models directly from binary representations of complex multivariate data and establish...
- The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill $199,730 under the Mathematical and Physical Sciences program (CFDA 47.049) on September 1, 2026, for research on interacting agent systems in optimal control and game theory. The recipient will develop mathematical frameworks for understanding large systems of interacting agents—such as economic systems, telecommunication grids, social networks, and generative AI...
- The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill $250,000 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop theoretical foundations, methodological approaches, and computational tools for modeling time-dependent systems characterized by unknown heterogeneity across multiple subjects. The project advances a unified statistical and machine learning framework for analyzing complex...
- The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill $100,000 on June 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop theory, methodology, and software for statistical inference on spatiotemporal rates of change and boundary assessment in large, complex spatiotemporally indexed datasets. The project, which runs through May 31, 2029, focuses on quantifying and understanding change within...
- The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Charlotte $163,903 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to advance theoretical foundations for efficient computational approximations of the Wasserstein metric in machine learning and artificial intelligence applications. The project delivers research on transportation cost spaces and group actions on Banach spaces, with objectives...
- This National Science Foundation (NSF) Division of Mathematical Sciences Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports the development of mathematical foundations and statistical methods for analyzing data with complex geometric structure. Awarded to the University of North Carolina at Chapel Hill on August 1, 2025, with total obligated funding of $299,978 through July 31, 2028, the project addresses fundamental challenges in data analysis for...
- The National Science Foundation Division of Mathematical Sciences awarded the University of South Carolina $700,000 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical foundations and algorithms for deep learning-based optimization through integration of optimal transport, information geometry, mean-field control, and spectral graph theory. The project addresses the absence of rigorous geometric frameworks for understanding...
- The National Science Foundation Division of Mathematical Sciences awarded Duke University $145,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to study structured random matrices for quantum chaos and manifold learning. The project investigates classes of structured random matrices motivated by two application domains: quantum chaos theory, which examines whether random matrix statistics govern the behavior of quantum systems through eigenvalue...
- The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill $350,000 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mimetic immersed boundary methods for fluid-structure interaction simulation. The project will create improved computational and mathematical tools to simulate systems where fluids and structures influence each other—applications spanning cardiovascular modeling, medical...
The National Science Foundation Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill $180,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical foundations and novel algorithms for structure-informed machine learning that incorporate intrinsic symmetries and group-equivariant neural networks. The project, performed in Chapel Hill, North Carolina, runs through July 31, 2029. Deliverables include rigorous uncertainty quantification and sample-complexity guarantees for symmetry-informed diffusion and flow-based models extending from fixed-dimensional settings to generative models for datasets containing samples of varying dimensionality; investigation of implicit bias induced by gradient-based training of group-equivariant neural networks; and comparative analysis of built-in equivariance versus data augmentation effects. The work aims to strengthen mathematical foundations of generative artificial intelligence with applications to image analysis, molecular design, and video generation, and includes workforce development through undergraduate and graduate research opportunities and new coursework in mathematical machine learning and deep generative models.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $180.0k | 8/4/26 |