Spring School Series: Models and Data

现代传感器和数字计算技术产生了大量的数据，这些数据携带的信息预计将对整个科学、技术和社会的几乎所有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”）的规模很大，但它们往往无法提供有关复杂过程的足够信息，以提出可靠的预测，这是任何技术设计所必需的。支配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。对复杂过程的资料要求越详细，模型就变得越复杂，随之而来的是数学和数值处理的后果。此外，在经典意义上识别适当的模型可能会变得越来越有限。因此，对数据和模型提供的信息进行适当的综合或综合将具有至关重要的长期意义。春季学校的中心目标是支持年轻的研究人员发展必要的概念方向。该项目有助于加速和培养对技术和社会具有高度影响的大多数专题研究领域的广泛专业知识。 代表相关领域的国际知名专家将提供六个两小时的整体讲座。这些讲座的目的，特别是在揭开重要的概念之间的相互联系，往往是不明显的不同领域。讲座将与分组会议和参与者积极参与的机会交错。 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，材料科学中的结构成像和建模中的正向和反向任务。我们的目标是将这些主题与最近的方法学发展配对，特别是那些能够科普所有上述主题所共有的空间高维挑战的方法学发展。举几个例子，稀疏高维多项式展开，深度神经网络，低秩和张量方法，可证明的模型降阶概念，稀疏促进正则化概念和贪婪策略。约30名年轻研究人员的目标出席率是保证与讲师进行最有效的互动。将维持一个互联网平台和一个共同的资料库，以便在讲习班之间收集和分享相关信息，并启动今后的合作。更多细节可在www.example.com上获得http://people.math.sc.edu/imi/dasiv/SpringSchool/This奖项反映了NSF的法定使命，并被认为值得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来支持。

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.