CAREER: Data-driven Numerical Linear Algebra: Foundations, Methods and Applications

As data science continues to evolve, there is a growing need to create new methods in numerical linear algebra to meet the unique complexities of modern data science problems, which are markedly different from traditional ones but also have the potential to lead to significant transformations in computational science. The main goal of this project is to develop a new set of data-driven numerical linear algebra algorithms that can adapt to both the model and the data, aiming to efficiently solve large-scale data analytics and scientific computing problems on today's advanced computing platforms. The methods developed through this project will make large and complex statistical and physical models more accessible, faster, more accurate, and more sustainable. The project also contains an extensive education plan to integrate K-12, undergraduate, and graduate students, educators, and scholars into computational mathematics and data science through workshops, tutorials, mini-symposia, internships, and collaborative research. Graduate students and undergraduate students will be trained on the topics of the this research project. This project focuses on developing novel data-driven numerical linear algebra tools for modern scientific computing and data science applications. The project focuses its efforts on three main areas: (1) developing data-driven numerical methods that can adjust their algorithmic components according to the model’s inherent structures and the data’s configuration; (2) developing data-driven hybrid solvers that maintain optimal performance across a range of problem classes; (3) designing robust mixed-precision numerical linear algebra kernels. High-performance software will be developed with carefully designed interfaces to facilitate their use in various applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.