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Gene Golub工业与应用数学学会（SIAM）暑期学校，题为“逆问题：不确定性下数据与模型的系统集成”，于2018年6月17日至30日在科罗拉多州布雷肯里奇举行。这个为期两周的暑期学校解决的基本问题是：我们如何通过模型的透镜从数据中进行最佳学习？当数据和模型不确定时（通常都是这样），我们该如何做到这一点呢？随着科学、工程、技术、医学和社会科学各个领域数据量的大规模爆炸，这些问题已经成为核心问题。暑期学校的目的是向研究生介绍这种逆问题的数学和计算方面，特别是强调贝叶斯推理框架内逆解中不确定性量化的现代发展。暑期学校将研究生与贝叶斯逆问题基础领域的专家聚集在一起。讲座以不适定性和正则化开始的综合格式为特色，通过数值优化开发了确定性反演的思想和工具，并阐述了现代贝叶斯观点的配方和解决方法，建立在几个确定性工具的基础上。整个讲座的重点是方法，可以扩展到由复杂的正向模型，如偏微分方程控制的反问题。上午的讲座由下午的动手实验室会议使用开源软件（hippylib和MUQ），实现了最先进的确定性和贝叶斯反演方法的补充，学校以学生项目演示结束。暑期学校的目的是增加现有的学术课程与教学贝叶斯逆问题，反映了该领域的数学和计算基础的相对较新的出现，需要整合从逆理论，偏微分方程，优化，概率，统计和计算的概念，并需要开发支持软件。这一观点对于通过模型解释时最大限度地从数据中获得信息至关重要。更多信息可以在httpps：//www.example.com上找到www.siam.org/students/g2s3/index.phpThis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。

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.