Spring School Series: Models and Data

春季学校系列：模型和数据

• 批准号: 1855853
• 负责人: Wolfgang Dahmen
• 金额: $ 2.49万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-03-15 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1855853&HistoricalAwards=false
• 关键词: Spring; Series; Models; Data

Modern sensor and digital computing technology has been generating an enormous wealth of data carrying information that is expected to have a transformative impact on virtually all branches of science, technology and society as a whole. The need to extract quantifiable information from such data sets has stimulated, in particular, a vibrant development of diverse mathematical methodologies. Despite the size of available data sites, often referred to as "Big Data", they nevertheless often fall short of providing enough information about a complex process to come up with reliable predictions, a must for any technological design. The physical laws that govern such processes can often be formulated in terms of mathematical models with excellent predictive capabilities. The more detailed information is sought on complex processes the more complex the models become with ensuing consequences for their mathematical and numerical treatment. Moreover, the identification of proper models in the classical sense may become increasingly limited. Therefore, a proper integration or synthesis of information provided by data as well as by models will be of paramount lasting importance. The central objective of the Spring School is to support young researchers in developing the necessary conceptual orientation. The project helps accelerating and fostering a broad based expertise in most topical research areas with high impact on technology and society. Internationally renowned experts, representing the relevant areas, will deliver six two-hour block lectures. These lectures aim, in particular, at unveiling important conceptual interconnections between different areas that are often not obvious. The lectures will be interlaced with break out sessions and opportunities for the participants to actively engage. This covers forward and inverse tasks in Uncertainty Quantification, parameter and state estimation, data assimilation, machine learning, structural imaging in material science, and modeling. The goal is to pair these topics with recent methodological developments, in particular, those that are able to cope with the challenge of spatial high-dimensionality shared by all the above topics. Examples, to name a few, are sparse high-dimensional polynomial expansions, deep neural networks, low-rank and tensor methods, certifiable model order reduction concepts, sparsity promoting regularization concepts, and greedy strategies. The target attendance of about 30 young researchers is to warrant a most effective interaction with the lecturers. An internet platform and a common repository will be maintained to collect and share relevant information during periods between the workshops and to initiate future collaboration. More details are available at http://people.math.sc.edu/imi/dasiv/SpringSchool/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.

现代传感器和数字计算技术已经产生了大量承载信息的数据，预计这些数据将对几乎所有科学、技术和整个社会的分支产生变革性影响。从这些数据集中提取可量化信息的需要特别刺激了各种数学方法的蓬勃发展。尽管可用的数据站点（通常被称为“大数据”）规模庞大，但它们往往无法提供有关复杂过程的足够信息，无法得出可靠的预测，而这是任何技术设计所必需的。控制这些过程的物理定律通常可以用具有出色预测能力的数学模型来表述。在复杂的过程中寻求越详细的信息，模型就越复杂，随之而来的是数学和数值处理的结果。此外，在经典意义上正确模型的识别可能变得越来越有限。因此，对数据和模型所提供的信息进行适当的整合或综合，将具有极其持久的重要性。春季学院的中心目标是支持年轻研究人员发展必要的概念方向。该项目有助于在大多数对技术和社会有重大影响的专题研究领域加速和培养广泛的专业知识。代表相关领域的国际知名专家将进行六场两小时的分组讲座。这些讲座特别旨在揭示不同领域之间通常不明显的重要概念联系。讲座将穿插分组讨论，并为参与者提供积极参与的机会。这涵盖了不确定性量化，参数和状态估计，数据同化，机器学习，材料科学结构成像和建模中的正向和反向任务。目标是将这些主题与最近的方法发展相结合，特别是那些能够应对所有上述主题共同面临的空间高维挑战的方法发展。例如，稀疏高维多项式展开、深度神经网络、低秩和张量方法、可认证模型降阶概念、稀疏促进正则化概念以及贪婪策略。约30名年轻研究人员的目标出席是保证与讲师最有效的互动。将维持一个互联网平台和一个共同储存库，以便在讲习班期间收集和分享有关资料，并开始今后的合作。更多的细节可在http://people.math.sc.edu/imi/dasiv/SpringSchool/This上获得，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。