Developing and analyzing variational methods and nonlinear, nonlocal regularization techniques for inverse problems under integro-differential equations, reflecting basic neural networks, will be an important research area in the coming years. This research connects to data assimilation, which has been greatly influenced by dynamical systems theory. When viewed as a collection of points in some possibly high-dimensional space, the shape and clusters of a dataset often reflects important patterns within data and optimal transport on graphs is an important tool in imaging and inverse problems.
People working on this subject within SACS are:
Post Doc / PhD