Project Grant 2555785

Federal Grant Award Summary

Georgetown University received a $201,757 Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), effective July 1, 2026, through June 30, 2029. The award funds theoretical and computational research on weak convergence effects of vector fields constrained by general linear partial differential equations (PDEs). The project delivers research outputs that establish the equivalence between A-quasiconvexity and weak lower semicontinuity of integral functionals, extending compensated compactness theory through an integrated approach combining algebraic geometry with real, complex, and Fourier analysis.

The award supports both fundamental research and workforce development products. On the research side, the project produces deep theoretical results validated through computational algorithms that leverage physics-constrained neural networks and Gaussian processes with GPU-accelerated computing to advance numerical methods for continuum models in science. Additionally, the funding provides structured research training opportunities for undergraduate and graduate students as well as postdoctoral researchers, preparing them for careers in artificial intelligence-related fields at both industrial and academic institutions. The integrated feedback loop between theoretical proofs and numerical experiments designed into the project methodology ensures practical validation of computational advances.