AUTHOR=Herzog Sebastian , Zimmermann Roland S. , Abele Johannes , Luther Stefan , Parlitz Ulrich TITLE=Reconstructing Complex Cardiac Excitation Waves From Incomplete Data Using Echo State Networks and Convolutional Autoencoders JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=Volume 6 - 2020 YEAR=2021 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2020.616584 DOI=10.3389/fams.2020.616584 ISSN=2297-4687 ABSTRACT=Echo state networks (ESNs) and convolutional autoencoders (CAEs) are applied to solve two data modelling tasks in cardiac dynamics: Recovering excitation patterns from from noisy, blurred or undersampled observations and reconstructing complex electrical excitation waves from mechanical deformation. Both approaches provide satisfying solutions, but CAEs turned out to be superior to ESNs in terms of reconstruction errors.