RTG: Applied Mathematics and Statistics for Data-Driven Discovery

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The simultaneous availability of large datasets, high performance computing, and modern machine learning algorithms holds great promise to enable scientists and engineers to rapidly discover hidden patterns in data, and to utilize these patterns to understand the natural world in order to solve pressing practical problems facing society. Realizing this promise requires addressing many mathematical and computational challenges: in framing scientific and technological problems for solution by data-driven approaches, in interpreting and analyzing data, and in designing efficient and reliable algorithms. There is an urgent need for mathematical scientists who are equally adept at wielding modern applied and computational mathematics on the one hand, and the tools of data-driven modeling, statistical inference, and scientific computing on the other. Furthermore, as interdisciplinary research and development become more common in industry, academia, and government, it is imperative that such mathematical scientists be generalists, able to communicate and work with specialists from diverse fields. This Research Training Group (RTG) addresses this need by increasing the number of mathematical scientists capable of working effectively at the interface of applied mathematics/statistics and modern data science. By focusing on specific applications requiring both mathematical innovation and data-driven modeling and by forming teams of mathematical scientists and domain experts, the RTG will enable trainees to address new challenges in innovative ways using their mastery of relevant mathematics, statistics and data science, and domain knowledge. Recognizing the challenges of advanced studies in STEM fields, the RTG will promote close, small-group mentoring at all levels. The expected outcome is mathematical scientists adept at working at disciplinary boundaries and intellectually equipped to tackle a wide range of scientific and technological challenges. It is expected that some of the trainees will continue in academia, where the proposed training activities can be improved and propagated; others will work in industry and government, applying their knowledge and skills to solve problems of practical significance.The RTG will support research on applied mathematics and data-driven modeling at the University of Arizona (UA), which is home to a large and vibrant mathematical science community. It is organized around a number of application-centered Working Groups, with foci ranging from analysis of gene regulation data to the modeling and forecasting of power grids. Each research project will impact both fundamental methodology and practical applications. The Working Groups are structured to enable vertically-integrated mentoring of RTG trainees at all levels -- undergraduate, graduate, and postdoctoral, and to enable trainees to work closely with Mathematics faculty and domain experts. Additional training activities include courses on foundational topics, e.g., optimization, machine learning, Monte Carlo methods, as well as practical skills such as software carpentry. By providing research training at the interface between the traditional domains of applied mathematics and the cutting-edge field of data-driven modeling, the RTG will both advance scientific knowledge and increase the number of US citizens and nationals with much-needed scientific and technological expertise.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.