Bridging the gap between discrete and continuous PDE in medical imaging

PI: Erkki Somersalo
Agency: NSF- DMS 2204618 Project  
Funding Amount: $299.998. Duration: 8/1/2022 – 7/31/2025.

A commonly encountered type of inverse problems is to estimate coefficient functions of a partial differential equation over a domain based on measurements of its solutions either inside or at the boundary of the domain. The computational treatment of such problems requires discretization of the problem, e.g., by using the finite element method. The discretization process generates a modeling error, and if not properly analyzed, the error can be detrimental due to the ill-posedness of the inverse problem in which small errors in data propagate to huge errors in the solution, see Figure. This project addresses the question by recasting the inverse problem in a novel way, where the discretization is part of the inverse problem. The methodology is based on hierarchical Bayesian modeling of the discretization and the modeling error. The methodology will be developed to address selected biomedical imaging applications.

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Material Data Science for Stockpile Stewardship Center of Excellence (MDS3 COE)

Faculty: Anirban Mondal
Agency: National Nuclear Security Administration (NNSA) – Department of Energy (DOE) 
Funding Amount: $14,200, 000 for Phase I, Duration: 09/15/2022 – 09/14/2027
Role: Co-I, PI – Roger French

Details about the Center of Excellence:
The vision of the MDS3 COE is to develop, demonstrate, and deploy novel Data Science tools, frameworks, codes, and computing infrastructure to advance our understanding of Materials degradation and the failure of materials, components, and subsystems using novel computer science and data science while empowering current NNSA employees and delivering a pipeline of the diverse, data-enabled workforce for the future. Phase II of the MDS3 COE will integrate the developed knowledge and workflows across the programs and agencies of the NNSA. 

There will be four research thrusts and one workforce thrust in the MDS3 COE. The Research Thrusts include Computing Infrastructure, Knowledge Management & Learning, Field-Lab Aging & Reliability, and Next Generation Component Design & Production. 

Dr. Mondal will be leading the Knowledge Management & Learning research thrust which will focus on developing scalable and privacy-preserving knowledge modeling and learning techniques. This includes developing a robust statistical learning framework for computer experiments, with the goal of developing both theoretical and methodological tools that cover the typical computer simulation pipeline and quantify the uncertainties in the estimation method.

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Mathematics and Physical Sciences-Collaboration Grants for Mathematicians

Faculty: Anirban Mondal
Agency: Simons Foundation
Project Title: Bayesian uncertainty quantification in remote sensing and infectious disease
modeling, and robust statistical methods in variable selection and clustering
Funding Amount: $42000, Duration: 09/012022-08/31/2027, Role: PI