Federal Project Grant Award Summary

The University of North Carolina at Chapel Hill received a $380,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049) for collaborative research on machine learning methodologies for stratified matrix manifolds under group actions. The award, effective July 1, 2026, through June 30, 2029, will deliver foundational mathematical theory, novel machine learning algorithms, and scientific applications that integrate topology, geometry, and machine learning to advance data-driven discovery. The project is organized into three primary deliverables: (1) mathematical and statistical foundations establishing stratified matrix manifolds and metrics while developing noise-robust dimensionality reduction techniques; (2) machine learning algorithms designed for equivariant dimensionality reduction, optimal transport, and flow-matching operations that preserve manifold structure across data strata; and (3) scientific applications demonstrating the resulting methods on computational neuroscience problems (neural stimulus space reconfiguration detection) and quantum science applications (symmetry-aware dimensionality reduction for Kohn-Sham density functional theory).

In addition to research deliverables, the project will generate intellectual capital through educational and workforce development outputs. The investigators will co-develop cross-institutional graduate seminars on machine learning and establish research experiences for undergraduates, training students in data-driven computation methodologies. These curriculum innovations and open science contributions are designed to strengthen national artificial intelligence competitiveness by advancing machine learning tools for complex biological and physical science datasets that have historically proven challenging for data reduction and generation tasks.