WITHDRAWN Operator Networks in Statistical Inverse Problems

Music City Center 

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).

statistical inverse problem

operator networks 

Section on Statistical Learning and Data Science