Project Grant 2515787
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $331,902 Project Grant to the Trustees of Boston University on August 15, 2023 under the Mathematical and Physical Sciences program (CFDA 47.049). The purpose of this 3-year grant is to develop rigorous mathematical analysis and theory for the training algorithms used in neural network models across various machine learning applications. The research will leverage stochastic analysis and weak convergence theory...
- The National Science Foundation (NSF) awarded a $270,000 Project Grant under the Mathematical and Physical Sciences Program (CFDA 47.049) to the Trustees of Indiana University for the project "Bayesian Methodologies for PDE Parameter Estimation: Model Problems, Algorithm Development and Applications." The project aims to develop advanced statistical methods to estimate unknown physical parameters from complex, sparse, and noisy data sets by incorporating first-principles physics into...
- The National Science Foundation (NSF) awarded a $599,474 Project Grant under the Computer and Information Science and Engineering (CFDA 47.070) program to the University of California, Santa Barbara (UCSB) to develop a real-time and energy-efficient neural network-based Partial Differential Equation (PDE) solver on a 2.5D photonic chip. The goal is to create a highly compressed and backward propagation-free training method for large-scale Physics-Informed Neural Networks (PINNs) that can be...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $107,860 Project Grant to the Regents of the University of Minnesota, Office of Sponsored Projects Administration, a non-profit 1862 land grant college, to conduct research under the NSF Mathematical and Physical Sciences program (CFDA 47.049). The research project will develop theoretical foundations for using machine learning methods to solve high-dimensional partial differential equations, emphasizing predictive...
- 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 Project Grant award of $494,628 from the National Science Foundation (NSF) Division of Mathematical Sciences to Brown University supports the development of effective computational tools and rigorous theoretical foundations for using neural networks to numerically solve partial differential equations (PDEs). The project aims to address the key challenges of ensuring accuracy, reliability, and intelligibility of neural network-based approaches for scientific computing applications, where the...
- This $149,999 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research into techniques for identifying hidden or unknown components in nonlinear differential equation models. The research aims to improve modeling and predictive capabilities for complex physical phenomena, such as fluid flows, turbulence, and weather prediction. The award to the Research Foundation of the City University of New York will provide...
- This $296,555 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support the development of reduced basis enhancements for neural networks and their application to quantum materials simulation. Specifically, the University of Massachusetts Dartmouth will combine traditional reduced basis methods with deep learning techniques to build an analysis-driven computational emulator for parameterized partial differential equations....
- The National Science Foundation (NSF) awarded a $689,835 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Brown University. The grant, with a performance period from December 1, 2024 to November 30, 2027, supports research focused on developing machine learning approaches for solving long-standing open problems in nonlinear partial differential equations, including dispersive, elliptic, and geometric frameworks. The project aims to unlock new mathematical...
- The National Science Foundation Division of Mathematical Sciences awarded a $255,783 Project Grant to the Trustees of Boston University for work titled "Multiscale Effects and Tail Events for Infinite-Dimensional Processes and Interacting Particle Systems." The three-year award runs from July 1, 2021 through June 30, 2024 under the Mathematical and Physical Sciences program (CFDA 47.049). The funding will support research examining multiscale phenomena and rare events in...
The National Science Foundation (NSF) awarded a $239,999 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to Trustees of Boston University. The grant, awarded on August 1, 2025, supports research to develop a statistical framework for drawing reliable inferences about parameters learned using physics-informed neural networks (PINNs) to solve and estimate the parameters of partial differential equations (PDEs) from noisy observations. The project aims to develop a novel debiasing technique to remove estimation bias in PINNs, facilitating more accurate inference about the physical parameters of interest. This research contributes to advancing the literature on squared-root-rate estimation of finite-dimensional functionals in semiparametric models, particularly in the context of PDE learning via neural networks. The project will be completed by July 31, 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $240.0k | 7/29/25 |