This $108,176 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research at the California Institute of Technology (Caltech) on interacting particle systems and their application to optimization, sampling, and filtering algorithms. The 5-year award, effective June 1, 2024, aims to develop a unified mathematical framework for these algorithms by reformulating them from the perspective of interacting particle systems....
This $275,000 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences supports the development of novel approaches to solving inverse problems. The goal is to enhance the accuracy and efficiency of computational methods used in critical applications like electrical impedance tomography, inverse scattering, and cryo-electron microscopy. This research has the potential to accelerate breakthroughs in molecular biology and rapid drug development, directly...
This three-year $100,000 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) will support the development of novel computational methods for large-scale inverse problems, randomized numerical linear algebra, and sparse principal component analysis at Arizona State University. The grant will advance efficient tools for solving large-scale inverse problems in scientific applications experiencing...
This $170,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences supports research on developing randomized algorithms for solving inverse problems and quantifying uncertainty in hierarchical Bayesian and dynamical inverse problems. Key goals include: (i) creating efficient algorithms to estimate uncertainty in the hyperparameters that govern Bayesian inverse problems, and (ii) developing new iterative methods leveraging randomization to...
This $170,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports collaborative research at North Carolina State University (NC State) to develop new randomized algorithms for solving large-scale inverse problems and quantifying uncertainty in hierarchical Bayesian models. The key research objectives are: (i) to create efficient algorithms for quantifying uncertainty in the hyperparameters governing Bayesian inverse...
This $616,000 Project Grant from the National Science Foundation (NSF) Division of Computing and Communication Foundations, under the CFDA program "Computer and Information Science and Engineering", supports research at the California Institute of Technology (Caltech) to address algorithmic and information-theoretic challenges in causal inference. The key objectives are to: Increase the range of applicability of causal inference methods by developing new algorithms and sample...
The National Science Foundation awarded Emory University a $346,631 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to develop methods for mixed precision arithmetic for solving large-scale ill-posed inverse problems. The University will focus on exploiting graphics processing units' mixed precision computing capabilities to efficiently compute approximate solutions to computationally intensive inverse problems. Key products include flexible computational...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on inverse boundary value problems and related mathematical techniques. The key research areas include: Electrical impedance tomography (EIT) for determining the conductivity of materials by making voltage and current measurements at the boundary. The research will address challenges in EIT such as partial data, anisotropic...
This $100,000 three-year Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research to advance numerical methods for large-scale inverse problems, sparse principal component analysis, and their applications. The awardee, Emory University, will collaborate with other institutions to develop novel approaches merging inverse problems, randomized numerical linear algebra, and sparse principal component analysis. This will...
The National Science Foundation Division of Mathematical Sciences awarded a $281,038 Project Grant to the California Institute of Technology (Caltech) for the project "FACTORIZATION HOMOLOGY AND LOW-DIMENSIONAL TOPOLOGY." The grant is part of the Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the nation's scientific enterprise through increasing knowledge and enhancing understanding of major problems. Under the...