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

University Of California - Merced, Merced CA

Investigators

Abstract

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 at https://www.siam.org/students/g2s3/index.php 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.