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....
This three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $582,898 to the Regents of the University of Minnesota for research on topics in the analysis of nonlinear partial differential equations. The research focuses on fluid mechanics equations like the Navier-Stokes equations, studying well-posedness, non-uniqueness, and related problems. It also examines steady-state...
This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) will provide $277,686 to the Regents of the University of Minnesota to develop advanced computational modeling and machine learning workflows for exploring the mechanical and electronic properties of 2D quantum materials. The project aims to enable rapid, automated, high-fidelity simulations of these materials, which are critical for advancing emerging...
This Project Grant award of $255,237 from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research by the Regents of the University of Minnesota to develop acceleration and preconditioning methods to improve the training efficiency of deep learning models. The research aims to leverage insights from numerical methods and linear algebra to speed up the computationally intensive and resource-demanding process of training large...
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 $450,000 from the National Science Foundation's Engineering program (CFDA 47.041) will support research on bi-level optimization for hierarchical machine learning problems. The award to the Regents of the University of Minnesota, conducting the work through their Office of Sponsored Projects Administration, aims to develop new approaches for modeling, analyzing, and innovating on a wide array of emerging machine learning applications using bi-level optimization...
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...
The National Science Foundation Division of Mathematical Sciences awarded $285,000 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to the Regents of the University of Minnesota for a project grant titled "Critical Phenomena in Coherent Structure Formation." The grant supports research from July 15, 2022 to June 30, 2025 to develop new analytical and computational tools to systematically analyze, predict, and validate models of self-organized coherent...
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 $285,669 Project Grant to Louisiana State University (LSU) under the Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049). The grant, awarded on July 15, 2025, will fund a research project focused on establishing a unified framework for adaptive sampling to enhance scientific machine learning algorithms. The project aims to optimize the selection of random samples in the training set for solving high-dimensional partial...