Observing spatio-temporal dynamics of excitable media using reservoir computing.

Area of Science:

• Computational modeling
• Dynamical systems theory
• Biophysics

Background:

• Excitable media models, like those for cardiac tissue, are crucial for understanding complex spatio-temporal phenomena.
• Accurate state estimation is vital for analyzing and controlling these systems, but often requires full state measurements.
• Existing methods may struggle with noisy data or require extensive spatial information.

Purpose of the Study:

• To introduce a novel dynamical observer for two-dimensional partial differential equation models of excitable media.
• To leverage Echo State Networks (ESNs) for cross-prediction of unmeasured state variables using only local spatial input.
• To validate the observer's efficacy on established models of biological systems.

Main Methods:

• Development of a dynamical observer framework incorporating Echo State Networks.
• Utilizing ESNs to process time-series data from local spatial regions to predict unmeasured state variables.
• Application and testing of the observer on the cubic Barkley model and the Bueno-Orovio-Cherry-Fenton model.

Main Results:

• The proposed observer successfully performs cross-prediction from observed time series to unmeasured state variables.
• The method demonstrates efficacy even with noisy data from complex models.
• Accurate reconstruction of chaotic electrical wave propagation in cardiac tissue models was achieved.

Conclusions:

• The Echo State Network-based dynamical observer offers an effective approach for state estimation in excitable media.
• This method advances the analysis of complex spatio-temporal systems by enabling prediction from localized, potentially noisy, measurements.
• The findings have implications for understanding and potentially controlling biological systems exhibiting wave propagation phenomena.