Spring School Series: Models and Data

University Of South Carolina At Columbia, Columbia SC

Investigators

Abstract

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.