Proximal and Invertible Neural Networks
Gabriele Steidl - TU Berlin
Proximal neural networks (PNNs) have the advantage of a controlled Lipschitz constant which make them interesting for many applications. We give an introduction into proximal neural networks, in particular their convolutional variant. Further, we are interested in invertible networks (see also normalizing flows) which can be used similarly as GANs to sample from a high dimensional unknown distribution by using a simpler one. We demonstrate an application of INNs in grazing incidence X-ray fluorescence, a non-destructive technique for analyzing the geometry and compositional parameters of nanostructures appearing e.g. in computer chips. We propose to reconstruct the posterior parameter distribution given a noisy measurement generated by the forward model by an appropriately learned invertible neural network. This network resembles the transport map from a reference distribution to the posterior. We demonstrate by numerical comparisons that our method can compete with established Markov Chain Monte Carlo approaches, while being more efficient and flexible in applications.
Gabriele Steidl received her PhD and Habilitation in Mathematics from the University of Rostock (Germany), in 1988 and 1991, respectively. From 1992 to 1993 she worked as a consultant at the Verband Deutscher Rentenversicherungsträger in Frankfurt am Main. From 1993 to 1996, she held a position as Assistant Professor at the Department of Mathematics at the TU Darmstadt. From 1996 to 2010, she was Professor at the Department of Mathematics and Computer Science at the University of Mannheim. From 2011 to 2020, she was Professor at the Department of Mathematics at the TU Kaiserslautern and Consultant of the Fraunhofer Institute for Industrial Mathematics. Since 2020, she is Professor at the Department of Mathematics at the TU Berlin. She worked as a Postdoc at the University of Debrecen (Hungary), the Banach Center Warsaw and the University of Zürich and was a Visiting Professor at the ENS Paris/Cachan and the Université Paris East Marne-la-Vallée and the Sorbonne. Since 2020 she is a member of the DFG Fachkollegium Mathematik and the Program Director of SIAG-IS (SIAM).
2021-05-25 at 3:00 pm