Towards Uncertainty Quantification for Goal-oriented Inverse Problems

Julianne Chung, Emory University
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Inverse problems arise in a wide variety of applications including biomedicine, environmental sciences, astronomy, and more, and computing reliable solutions to large-scale problems remains a challenge. In this talk, we describe some new approaches that harness recent advancements in the field of machine learning for large-scale inverse problems. First, we describe deep neural networks (DNNs) for efficient hyperparameter estimation. Second, we describe variational encoder-decoder (VED) networks for uncertainty quantification. In particular, we are interested in goal-oriented inverse problems, where the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of these approaches.

Bio: Dr. Julianne Chung is an Associate Professor in the Department of Mathematics at Emory University. Prior to joining Emory in 2022, she was an Associate Professor in the Math Department at Virginia Tech and an Assistant Professor at the University of Texas at Arlington. She was an NSF Mathematical Sciences Postdoctoral Research Fellow at the University of Maryland at College Park in the Department of Computer Science. She received her PhD in 2009 at Emory University, during which she was supported by a Department of Energy Computational Science Graduate Fellowship. She has received many prestigious awards including the Frederick Howes Scholar in Computational Science award, an NSF CAREER award, and an Alexander von Humboldt Research Fellowship.

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