2018 Gene Golub SIAM Summer School: Inverse Problems: Systematic Integration of Data with Models under Uncertainty

该奖项支持美国博士生参加2018年6月17日至30日在科罗拉多州布雷肯里奇举行的2018年吉恩·戈卢布工业和应用数学学会(SIAM)暑期学校，题为“逆问题：不确定性下的数据与模型的系统集成”。这个为期两周的暑期班解决的根本问题是：我们如何通过模型的镜头以最佳方式从数据中学习？当数据和模型不确定(通常都是这样)时，我们如何做到这一点？随着科学、工程、技术、医学和社会科学各个领域的数据量的巨大爆炸，这些问题已经成为核心。暑期班旨在向研究生介绍此类逆问题的数学和计算方面，特别是强调在贝叶斯推理框架内对逆解的不确定性进行量化的现代发展。暑期班将研究生和贝叶斯反问题基础领域的专家聚集在一起。这些讲座的特点是以病态和正则化开始的综合格式，通过数值优化开发确定性反演的思想和工具，并在几个确定性工具的基础上阐述现代贝叶斯观点的公式和求解方法。整个讲座的重点是方法，可以扩展到由复杂的正向模型管理的反问题，如偏微分方程式。上午的课程与下午使用开放源码软件(Hippylib和MUQ)的动手实验室课程相辅相成，该软件实现了最先进的确定性和贝叶斯反转方法，学校最后以学生项目报告结束。暑期班的目的是增加现有的学术课程，教授贝叶斯逆问题，反映该领域相对较新的数学和计算基础，需要整合逆理论、偏微分方程、最优化、概率、统计和计算的概念，以及开发支持软件的需要。这一观点对于通过模型解释时最大化从数据中获得的信息至关重要。更多信息可以找到athttps://www.siam.org/students/g2s3/index.phpThis奖项反映了美国国家科学基金会的法定使命，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。

This award supports the participation of US-based PhD students in the 2018 Gene Golub Society for Industrial and Applied Mathematics (SIAM) Summer School entitled "Inverse Problems: Systematic Integration of Data with Models under Uncertainty," taking place June 17-30, 2018 in Breckenridge, Colorado. The fundamental question addressed by this two-week summer school is: How do we optimally learn from data through the lens of models? And how do we do so when the data and models are uncertain (as they usually are)? These questions have become central with the massive explosion of data volumes across all areas of science, engineering, technology, medicine, and the social sciences. The summer school aims to introduce graduate students to the mathematical and computational aspects of such inverse problems, particularly modern developments that emphasize the quantification of uncertainty in the inverse solution within the framework of Bayesian inference. The summer school brings graduate students together with experts in foundational areas of Bayesian inverse problems. The lectures feature an integrated format that begins with ill-posedness and regularization, develops the ideas and tools for deterministic inversion via numerical optimization, and elaborates formulations and solution methods for the modern Bayesian perspective, building on several of the deterministic tools. The focus throughout the lectures is on methods that can scale to inverse problems governed by complex forward models, such as partial differential equations. Morning lectures are complemented by afternoon hands-on laboratory sessions using open-source software (hippylib and MUQ) that implements state-of-the-art deterministic and Bayesian inversion methods, and the school concludes with student project presentations. The summer school aims to augment existing academic curricula with instruction in Bayesian inverse problems that reflects the relatively recent emergence of the mathematical and computational foundations of the field, the need to integrate concepts from inverse theory, partial differential equations, optimization, probability, statistics, and computing, and the need to develop supporting software. This perspective is critical to maximizing the information gained from data when interpreted via models.More information can be found athttps://www.siam.org/students/g2s3/index.phpThis 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.