## Applied Mathematics

•  Nir Sochen, University of Tel Aviv
•  Unsupervised deep learning of forward and inverse solutions for PDE-based imaging; zoom link @ https://sites.google.com/view/minds-seminar/home
•  08/27/2020
•  2:30 PM - 3:30 PM
•

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)  Many imaging modalities are based on inverse problems of physical processes that are given as PDEs. Traditional methods for solving these PDE-based forward and inverse problems are based on discretizations of the domain. Deep learning methods are based on an excessive amount of input-output pairs. Both approaches encounter problems either by numerical instabilities and by being limited to low dimensions or by the lack of sufficient data. We suggest an alternative method of unsupervised deep learning method were the network parametrizes the solution and the loss function minimizes the deviation from the PDE. The input set are points sampled randomly in the domain and the output is the deviation from the PDE, namely zero. One key issue in the loss function is the introduction of the L_infty term that guaranty the uniform convergence of the network to the solution. We demonstrate our method on the Electrical Impedance Tomography (EIT).

## Contact

Department of Mathematics
Michigan State University