Project Grant 2152780

This three-year, $200,000 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program will fund the development of more computationally efficient methods for solving high-dimensional problems that commonly arise in scientific, engineering, and commercial computing. Specifically, the grant recipient, Stanford University, will improve randomized quasi-Monte Carlo sampling techniques and develop a median-of-means strategy to better handle problems involving large numbers of input variables, such as those seen in graphics rendering, financial modeling, and pollution modeling. The project combines these randomized quasi-Monte Carlo methods with active subspace techniques from uncertainty quantification to reduce effective dimensionality. Outcomes will include training doctoral students and disseminating results, with the goal of enhancing understanding of major technical challenges and strengthening the U.S. scientific enterprise.