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.

Topics
Dynamical systems, Chaotic dynamics, State functions, Wave propagation, Artificial intelligence, Artificial neural networks, Machine learning, Data visualization, Operator theory
© 2018 Author(s).
2018
Author(s)
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