Organizing Committee
Abstract

Interested in discussing cutting edge research ideas with both peers and leaders in their field?

Interested in broadening your professional network across the mathematical sciences?

Interested in the opportunity to present your ideas and hear about funding opportunities from program officers?

Idea-Lab is a one-week program aimed at 15 early career researchers (within five years of their Ph.D.) that will focus on a topic at the frontier of research. Participants will be exposed to a problem whose solution may require broad perspectives and multiple areas of expertise. Senior researchers will introduce the topic in tutorials and lead discussions. The participants will break into teams to brainstorm ideas, comprehend the obstacles, and explore possible avenues towards a solution. The teams will be encouraged to develop a research program proposal. On the last day, they will present their ideas to one another and to a small panel of representatives from funding agencies for feedback and advice.

IdeaLab applicants should be at an early stage of their post-Ph.D. career. A CV, research statement, and two reference letters are required.

Confirmed Speakers & Participants

IdeaLab Topic

Inverse Problems and Uncertainty Quantification

Inverse problems arise in an enormous variety of science and engineering applications. Examples range from understanding the dynamics of Antarctic ice sheets to developing predictive models of combustion emissions. In all these applications, model parameters must be estimated from noisy and indirect observational data. Uncertainty is integral to this endeavor: observational errors, model errors, and issues of ill-posedness yield uncertainties in model parameters. More broadly, the solution of inverse problems can be viewed as the interpretation of data through the lens of models that capture key relationships between measured quantities, the state and parameters of a system, and the ultimate quantities of interest to the modeler.

Bayesian statistical approaches to inverse problems offer the ability to endow model parameters and subsequent predictions with quantified uncertainties, reflecting both prior information and the information available in observations. Quantifying uncertainty in predictions of interest in turn enables coherent approaches to model-based decision making. While the past several years have seen significant advances in both the theoretical formulation of Bayesian inverse problems and the development of effective computational tools for their solution, many important and long-standing challenges remain: methods for efficient posterior exploration in high or infinite-dimensional parameter spaces, algorithms that exploit the structure of expensive PDE-based forward models, algorithms for parsing and reducing "big data" in the context of inversion, the construction of controlled approximations to the posterior distribution and its constituent models, the development of physically meaningful yet mathematically coherent prior distributions, and methods for incorporating model errors into the inverse solution and subsequent predictions.

The goal of this IdeaLab is to lay out the fundamentals of uncertainty quantification for inverse problems in a relatively rapid but hands-on manner, so that participants can understand and fluently discuss the current state of the art. We will also present connections to classical (regularization-based) inverse problems. We will then brainstorm projects focusing on new methodological approaches and new applications. The session will benefit from collaboration among participants with diverse mathematical and computational interests, ranging from statistics and machine learning to optimization and numerical PDE, as well as interests across a broad set of science and engineering application areas.

Satellite observations of surface ice flow velocity used to solve Antarctic ice sheet inverse problem, along with a model of ice flow as a non-Newtonian fluid
Inferred basal friction parameter field (warm colors imply low resistance to sliding at base of ice sheet)

Workshop Schedule

Monday, July 6, 2015
TimeEventLocationMaterials
8:30 - 8:35Registration11th Floor Conference Room 
9:00 - 10:30Deterministic inversion I121 South Main Street, 11th Floor Conference Room 
10:30 - 11:00Coffee/Tea Break11th Floor Conference Room 
11:00 - 12:30Deterministic inversion II11th Floor Conference Room 
12:30 - 2:00Lunch Provided11th Floor Conference Room 
2:00 - 5:00Deterministic inversion III11th Floor Conference Room 
5:15 - 6:30Welcome Reception11th Floor Collaborative Space, ICERM 
Tuesday, July 7, 2015
TimeEventLocationMaterials
9:00 - 10:30Bayesian inversion IICERM 11th Floor Conference Room 
10:30 - 11:00Coffee/Tea BreakICERM 11th Floor Conference Room 
11:00 - 12:30Bayesian inversion IIICERM 11th Floor Conference Room 
12:30 - 2:00Break for Lunch   
2:00 - 3:30Bayesian inversion IIIICERM 11th Floor Conference Room 
3:30 - 4:00Coffee/Tea BreakICERM 11th Floor Conference Room 
4:00 - 5:00Bayesian inversion IVICERM 11th Floor Conference Room 
Wednesday, July 8, 2015
TimeEventLocationMaterials
9:00 - 12:00Working GroupsICERM 10th Floor Collaborative Space 
12:00 - 2:00Break for Lunch   
2:00 - 5:00Working GroupsICERM 10th Floor Collaborative Space 
Thursday, July 9, 2015
TimeEventLocationMaterials
9:00 - 12:00Working GroupsICERM 10th Floor Collaborative Space 
12:00 - 2:00Break for Lunch   
2:00 - 5:00Working GroupsICERM 10th Floor Collaborative Space 
Friday, July 10, 2015
TimeEventLocationMaterials
10:00 - 10:10Introduction - Homer Walker, ICERMDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
10:10 - 10:35Uncertainty Quantification in Image Registration - Andreas Mang, Masha Mirzagar, Lars Ruthotto, Stephen WuDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
10:35 - 11:00From Imaging to Treatment: Propagating Uncertainty in Medical Treatment - Andrea Arnold, Kenny Chowdhary, Tulin Kaman, Umberto Villa Digital Scholarship Lab (10 Prospect Street, Providence, RI) 
11:00 - 11:10Short BreakDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
11:10 - 11:35Object detection via scattering: a Bayesian approach - Sergios Agapiou, Jerrad Hampton, Georgios Karagiannis, Jayanth Jagalur MohanDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
11:35 - 12:00A convex approach to reduced model based inversion - Ali Ahmed, Jonghyun Lee, Qin LiDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
12:00 - 12:15Group PhotoDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
12:15 - 1:00Lunch ProvidedDigital Scholarship Lab (10 Prospect Street, Providence, RI) 
1:00 - 2:20Program Officer PanelDigital Scholarship Lab (10 Prospect Street, Providence, RI)