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

2018 Gene Golub SIAM 暑期学校：反问题：不确定性下数据与模型的系统集成

• 批准号: 1834756
• 负责人: Noemi Petra
• 金额: $ 2万
• 依托单位: University of California - Merced
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-06-15 至 2019-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1834756&HistoricalAwards=false
• 关键词: 2018; Gene; Golub; SIAM; Summer; 2018; Gene; Golub; SIAM; Summer

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.

该奖项支持总部位于美国的博士学位学生参与2018年基因戈鲁布工业和应用数学学会（SIAM）暑期学校，题为“逆问题：与不确定性下的模型的系统整合与模型的系统整合”，于2018年6月17日至30日在科罗拉多州的布雷肯里奇举行。这个为期两周的暑期学校解决的基本问题是：我们如何通过模型镜头从数据中最佳学习？当数据和模型不确定时，我们该怎么办？这些问题已成为科学，工程，技术，医学和社会科学各个领域的数据量的大规模爆炸量的核心。暑期学校旨在向研究生介绍此类反问题的数学和计算方面，尤其是现代发展，这些发展强调了贝叶斯推论框架内反向解决方案中不确定性的量化。暑期学校将研究生与贝叶斯逆问题基础领域的专家组成。演讲具有综合格式，始于不适合性和正则化，通过数值优化开发了确定性反转的思想和工具，并阐述了现代贝叶斯观点的公式和解决方案方法，建立在确定性工具的基础上。整个讲座中的重点是可以扩展到可以扩展到由复杂的远期模型（例如部分微分方程）所控制的反问题的方法。下午的讲座是通过使用开源软件（Hippylib和MUQ）实现最先进的确定性和贝叶斯倒置方法的下午动手实验室会议来补充的，而学校则以学生项目的演讲结束。暑期学校的目标是通过贝叶斯反问题的指导来增强现有的学术课程，这反映了该领域的数学和计算基础相对较新的出现，需要从逆理论，部分微分方程，优化，概率，统计数据以及计算以及开发支持软件的需要中整合概念的需求。通过模型解释时，这种观点对于从数据中获得的信息最大化至关重要。可以找到更多信息。