Project Grant 2307465

Award Date 7/1/23
Completion Date 6/30/26
Dollars Obligated $308K
Federal Grant Program
47.049
Assistance Type
Project Grant
Place of Performance
Atlanta, GA 30332, USA
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The Georgia Institute of Technology Research Corporation (Georgia Tech) will receive $307,710 under a three-year Project Grant from the National Science Foundation (NSF) Division of Mathematical Sciences. The grant falls under the NSF Mathematical and Physical Sciences program (CFDA 47.049), which aims to strengthen the nation's scientific enterprise through increased understanding of major problems.

Specifically, Georgia Tech will develop novel formulations and rigorous error estimates for using deep neural networks (DNNs) to solve an important class of partial differential equations called Wasserstein geometric flows. The research is expected to advance the mathematical underpinnings of DNN-based approaches and enable effective computational algorithms for solving these PDEs in practice. Key objectives include establishing parameterized Wasserstein sub-manifolds and developing computationally efficient formulations for parameterized Wasserstein geometric flows, with associated convergence analysis and error estimates. Findings will connect to classical PDEs like the Schrödinger and Fokker-Planck equations. The research also provides topics to train the next generation of mathematicians and engineers in this interdisciplinary field.

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