Collaborative Research: Cost-Efficient and Confident Sampling for Modern Scientific Discovery

There are now novel sources of high-quality data for tackling a broad array of pressing scientific and engineering problems that need to be solved to improve our quality of life. However, such high-fidelity data often comes from costly simulations, limiting the available data. Thus, developing cost-efficient sampling methods combined with rigorous, data-driven error measures for the resulting models is critically important. This project combines ideas from computational mathematics and statistics to discover these cost-efficient and confident sampling methods. Students involved in this project will be educated to become the next generation of science-based computational researchers who can adeptly work in diverse and multi-disciplinary scientific teams pushing forward the frontiers of scientific knowledge. This project develops a framework featuring methodologies (with supporting theory and algorithms) that extend classical low discrepancy (i.e., highly stratified) sampling techniques for a broad range of challenging scenarios encountered in modern scientific problems, including cost-efficient Bayesian inference, efficient subsampling of massive data, multi-fidelity modeling, and density estimation. These methodologies include Bayesian sampling for expensive posteriors, adaptive multifidelity algorithms, big data subsampling, and distribution, density, and quantile estimation. The major emphasis is to demonstrate the effectiveness of these methods for accelerating scientific discoveries, especially for the PIs’ ongoing collaborations on the study of heavy-ion collisions and real-time engine control of unmanned aircraft vehicles, but also for new collaborations that will be developed over the project. Such collaborations will be further strengthened via our open-source Python QMC library QMCPy. 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.