RTG: Computational Mathematics for Data Science

计算和数据支持的科学已经成为科学的第三支柱，完成了理论和实验。科学计算方面的突破、可用数据的爆炸性增长以及我们制定数学模型并根据测量数据进行校准的能力，推动了它的成功。最近的成功案例从数值天气预报到语音识别，从过去几年在准确性方面取得了巨大成就的数字天气预报，到过去十年通过系统地从数据中学习而得到显著改进的语音识别。该项目的目的是实施一个以数据科学计算数学为中心主题的全面的纵向综合研究培训小组(RTG)。计算数学和数据科学除了对美国具有基础性和战略重要性(例如，对于开发新的药物、技术和国防能力)外，都是可以产生巨大社会影响并将吸引广泛学生的领域。该项目的RTG主题包括从统计数据同化到机器学习的各种应用，这些应用是我们这个时代最具变革性的技术之一，并通过从药物发现到无人驾驶汽车的许多潜在应用吸引了大量公众的兴趣。尽管取得了许多进展，但仍然迫切需要更多的数学理论和严谨的数学知识，这为各级数学家提供了充足的研究机会，从本科生、研究生、博士后和高级科学家。该项目将每年支持3名研究生、1.5名本科生和至少1名博士后。数据科学的核心是使用数学方法和计算方法从数据中提取知识和信息。利用数据革命需要在理论、模型和计算算法方面取得新的数学突破。尤其需要突破，使数学家和应用科学家能够以有效、可靠和可解释的方式分析和综合更大、更复杂的数据集。为此，本项目中进行的研究将统一和进一步发展从数据同化到机器学习等各种应用中使用的数学理论和计算工具。这一综合方法将以数学、计算科学和数据科学的知识为基础，并做出新的贡献。将特别关注深度学习和数据同化的数学及其在医学(心脏建模、医学成像)、天气和环境(飓风风暴潮建模)和疾病暴发建模等影响领域的应用。这些领域的共同主线是它们的数学基础，最重要的是微分方程、最优化、线性代数和来自计算科学的高级技术，如并行和分布式计算。这一RTG计划以为期一年的研究主题为基础，包括上述一个或多个核心研究主题。培训将是多方面的，包括教育，潜在的职业技能和经验，软技能，科学诚信，以及促进对多样性的欣赏。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.