Observing spatio-temporal dynamics of excitable media using reservoir computing

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018

Zimmermann, R. S. and Parlitz, U. (2018). Observing spatio-temporal dynamics of excitable media using reservoir computing. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(4), 043118.

We present a dynamical observer for two dimensional partial differential equation models describing excitable media, where the required cross prediction from observed time series to not measured state variables is provided by Echo State Networks receiving input from local regions in space, only. The efficacy of this approach is demonstrated for (noisy) data from a (cubic) Barkley model and the Bueno-Orovio-Cherry-Fenton model describing chaotic electrical wave propagation in cardiac tissue.

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