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MAE Graduate Seminar Speaker Series

proudly presents

Anuj Abhishek, PhD

Case Western Reserve University

Abstract

Neural operators such as Deep Operator Networks (DeepONet) and Convolutional Neural Operators (CNO) have been shown to be fairly useful in approximating an operator between two function spaces. In this talk, we at first show that they can be used to approximate operators that are maps between more general Banach spaces (not necessarily just function spaces) and which appear in various important medical imaging problems. Following recent developments in the field, we derive universal approximation theorem type results for two different network implementations that are used for learning the types of operators that turn up in imaging modalities such as EIT, DOT and QPAT. We then show how these operator learning frameworks may be used for direct inversion as well as may be used as surrogate models for the likelihood evaluation in Bayesian inversion. This is based on joint works with Thilo Strauss (Xi’an Jiaotong-Liverpool University) and Taufiquar Khan and Sudeb Majee (UNC Charlotte).

Bio

Anuj Abhishek is an Assistant Professor of Mathematics at Case Western Reserve University. Before this, Anuj Abhishek was postdoctoral research fellow at UNC Charlotte and at Drexel University. He received his PhD from Tufts University and was advised by Prof. Todd Quinto. Dr. Abhishek’s research interests lie with inverse problems, microlocal analysis and integral geometry.

Invited by: Susanta Ghosh