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 (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 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 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...
This National Science Foundation (NSF) project grant under the Computer and Information Science and Engineering (CISE) program (CFDA 47.070) was awarded to Carnegie Mellon University in the amount of $600,000 on August 15, 2024. The project will build mathematical foundations for using machine learning methods, specifically neural networks, to improve the process of solving partial differential equations (PDEs) and leverage PDEs as a tool for generative modeling. The research will explore issues...
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 (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...
This $1,197,878 project grant from the National Science Foundation's Office of Advanced Cyberinfrastructure will support the development of Evolutional Deep Neural Network algorithms for solving high-dimensional partial differential equations. Funded under the Computer and Information Science and Engineering program (CFDA 47.070), this collaboration between U.S. and French researchers aims to accelerate computational predictions of complex phenomena across multiple disciplines. Specifically, the...
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...