Project Grant 2510829
- This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) is focused on developing novel mathematical theories and computational methods to efficiently solve high-dimensional partial differential equations (PDEs) and learn PDE solution operators using deep neural network-based approaches. The $100,000 award to the Georgia State University Research Foundation Inc. will support research across three key objectives: (1) supervised learning...
- The National Science Foundation (NSF) awarded a $299,998 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to Georgia Tech Research Corporation to conduct fundamental research on the dynamics of nonlinear partial differential equation (PDE) systems that model fluid flow and nonlinear waves. The research will focus on analyzing the local dynamics near steady states in incompressible fluid PDEs with free surfaces, as well as a class of nonlinear...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to Duke University on August 1, 2023 under the Mathematical and Physical Sciences program (CFDA 47.049) to support innovative numerical methods for solving high-dimensional partial differential equations (PDEs). The key objectives of the 3-year project are to: (1) design and analyze neural-network parametrization for high-dimensional functions with symmetry constraints, and (2) develop and...
- This $597,791 Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program (CFDA 47.070) will support collaborative research at Duke University to explore the synergies between machine learning and partial differential equations (PDEs). The research aims to strengthen the use of machine learning methods, specifically neural networks, for improving PDE solving processes, as well as to further elucidate the role of PDEs in...
- This Project Grant award of $150,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into the asymptotic behavior of partial differential equations (PDEs) across a range of scientific applications. The Principal Investigator (PI) will investigate long-term propagation and front structure in reaction-diffusion equations, analyze limits of stochastic PDEs in physical systems, and study the effects of viscosity on shock...
- This Project Grant award of $200,000.00 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports a research project that develops methods for the qualitative and quantitative study of nonlinear partial differential equations (PDEs) in finite and infinite dimensional state spaces. The research emphasis is on the theory of mean field games, viscosity solutions techniques, and applications to areas such as traffic models, portfolio selection,...
- This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program provides $140,889 to Texas A&M University to conduct research connecting machine learning and numerical methods for partial differential equations. The key objectives are to leverage deep learning techniques to improve numerical methods for PDEs, and apply the theoretical understanding of finite element methods to better comprehend the success of deep neural networks....
- 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...
- This $268,602 federal Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports an interdisciplinary research project led by the Regents of the University of Michigan. The research aims to develop new mathematical tools based on partial differential equations (PDEs) and apply them to address practical challenges in mathematical finance and game theory. Key focus areas include: 1) using infinite-dimensional PDEs to demonstrate...
- This $399,583 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research to develop numerical algorithms that can estimate solutions to partial differential equations (PDEs) without full boundary condition information. The research aims to enable improved modeling and forecasting capabilities across various applications, including meteorology, biology, and engineering design. The primary awardee, Texas...
This $200,000 Project Grant was awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports a collaborative research project to develop novel mathematical theories and computational methods for efficiently solving high-dimensional partial differential equations (PDEs) and learning solution operators using deep neural network-based approaches. The key objectives are to: 1) propose a supervised learning method for solving high-dimensional Hamilton-Jacobi equations using a density coupling strategy, 2) develop a parameter control framework for rapid simulations of high-dimensional evolution PDEs across varying initial/boundary conditions, and 3) introduce a deep tangent bundle method for efficient high-dimensional function approximation and PDE simulation. The research aims to address major challenges in solving high-dimensional PDEs, which have widespread applications in modeling physical, chemical, biological, financial, and engineering systems. The project will be carried out by Georgia Tech Research Corporation, a non-profit research organization, over a period of 3 years from September 2025 to August 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $200.0k | 8/14/25 |