Stability Aspects of Imaging and Scientific Machine Learning

Deep learning algorithms have emerged as powerful tools in different applications including image classification, medical imaging and the solution of PDEs. The first part of this talk focuses on stability to adversarial attacks in imaging. While it is known that successful attacks can be designed for data-driven methods, we find that also classical regularization methods can be adversarially attacked. The second part is devoted to stability of operator learning with respect to discretizations. We establish a novel concept of neural operators that by-passes aliasing. These Representation equivalent Neural Operators (ReNOs) link operators between infinite-dimensional spaces to their discrete realizations. As a concrete architecture, we propose Convolutional Neural Operators (CNOs).