RTG: Computational Mathematics for Data Science

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Computational and data-enabled science has become the third pillar of science, completing theory and experimentation. Its success has been fueled by breakthroughs in scientific computing, the explosion of available data, and our ability to formulate mathematical models and calibrate them to measured data. Recent success stories range from numerical weather prediction, which has seen tremendous achievements in accuracy over the past years, to speech recognition, which has dramatically improved in the last decade by systematically learning from data. The aim of this project is to implement a comprehensive vertically integrated Research Training Group (RTG) on the central theme of Computational Mathematics for Data Science. In addition to being areas of fundamental and strategic importance to the United States (e.g., for the development of new medicines, technologies, and defense capabilities), both computational mathematics and data science are areas that can have a tremendous societal impact and will attract a broad range of students. The RTG themes of this project include applications ranging from statistical data assimilation to machine learning, which are among the most transformative technologies of our times and have captured substantial public interest with many potential applications from drug discovery to driverless cars. Despite many advances, there still is a pressing need for more mathematical theory and rigor, which provides ample research opportunities for all levels of mathematicians, from undergraduate students, graduate students, postdocs, and senior scientists.This project will support 3 graduate students per year, 1.5 undergraduate students per year and at lease 1 postdoc per year. At its core, data science uses mathematical methods and computational approaches to extract knowledge and information from data. Harnessing the data revolution requires new mathematical breakthroughs in the form of theory, models, and computational algorithms. Breakthroughs are particularly needed to enable mathematicians and application scientists to analyze and synthesize larger and more complex datasets in an effective, reliable, and explainable manner. To this end, the research conducted in this project will unify and further develop the mathematical theory and computational tools used in applications ranging from data assimilation to machine learning. This comprehensive approach will be based on knowledge from, and make novel contributions to mathematics, computational science, and data science. Particular focus will be on the mathematics of deep learning and data assimilation and their application in impactful areas of medicine (cardiac modeling, medical imaging), the weather and environment (hurricane storm surge modeling), and disease outbreak modeling. Common threads in these areas are their mathematical foundations, most importantly differential equations, optimization, linear algebra and advanced techniques from computational science, such as parallel and distributed computing. This RTG program is anchored around year-long research themes that include one or more of the above mentioned core research themes. Training will by multi-faceted, to include education, potential career skills and experiences, soft skills, scientific integrity, and promoting an appreciation for diversity.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.