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...
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 fund collaborative research between Duke University and its partners to explore the synergies between machine learning and partial differential equations (PDEs). The key objectives are to: 1) investigate the representational power, inductive biases, and numerical stability of neural network architectures for PDE solving, and 2)...
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...
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...
The National Science Foundation (NSF) awarded a $689,835 Project Grant to Brown University under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The grant aims to develop machine learning approaches for solving long-standing open problems in nonlinear partial differential equations, including dispersive, elliptic, and geometric frameworks. The project will also advance the heuristics behind machine learning numerics for such equations, guided by new mathematical...
This National Science Foundation (NSF) Computer and Information Science and Engineering (CISE) Federal Grant Program (CFDA 47.070) award to Carnegie Mellon University (CMU) provides $600,000 in funding to conduct collaborative research on the use of machine learning for solving partial differential equations (PDEs) and the use of PDEs for generative AI models. The project aims to build mathematical foundations around key questions at the intersection of machine learning and PDEs, exploring...
This NSF-funded project grant under the Mathematical and Physical Sciences (CFDA 47.049) program aims to advance the fields of geometric machine learning and numerical partial differential equations (PDEs). The $121,190 award to Emory University, spanning from August 2024 to July 2027, will focus on improving the scalability of graph neural network (GNN) algorithms to handle large datasets and accelerating numerical PDE simulations using GNN components. The research team will develop...
This project grant award of $600,000 from the National Science Foundation's (NSF) Office of Advanced Cyberinfrastructure under the Computer and Information Science and Engineering (CFDA #47.070) program will support the development of hybrid models that combine deep neural networks and high-fidelity partial differential equation (PDE) solvers. The goal is to create a system that maintains the accuracy of PDE models while leveraging the speed of neural networks to enable accelerated solutions for...
The National Science Foundation awarded a $225,000 Project Grant to Texas A&M University under the Mathematical and Physical Sciences program (CFDA 47.049) for the period of November 1, 2021 through October 31, 2024. The grant funds collaborative research on new perspectives for deep learning by bridging approximation, statistical, and algorithmic theories. The Mathematical and Physical Sciences program aims to advance scientific knowledge and understanding in core areas of mathematics and...