Data-Driven Modeling and Prediction of Complex Spatio-Temporal Dynamics in Excitable Media

Abstract

Spatio-temporal chaotic dynamics in a two-dimensional excitable medium is (cross-) estimated using a machine learning method based on a convolutional neural network combined with a conditional random field. The performance of this approach is demonstrated using the four variables of the Bueno-Orovio-Fenton-Cherry model describing electrical excitation waves in cardiac tissue. Using temporal sequences of two-dimensional fields representing the values of one or more of the model variables as input the network successfully cross-estimates all variables and provides excellent forecasts when applied iteratively.

Reconstructing Complex Cardiac Excitation Waves From Incomplete Data Using Echo State Networks and Convolutional Autoencoders

“…Also with the CAE several options exist to improve the performance even more. Instead of the MAE in the loss function one could use an adaptive robust loss function [59] or the Jensen-Shannon divergence [19]. The weights of the CAE could be optimized with a stochastic gradient descend approach instead of the ADAM algorithm [57].…”

“…Hoffman et al reconstructed electrical wave dynamics using ensemble Kalman filters [16,17]. In another approach, it was shown that echo state networks [18] and deep convolutional neural networks [19,20] provide excellent cross estimation results for different variables of a mathematical model describing complex electrical excitation waves during cardiac arrhythmias. Following this approach, Christoph and Lebert [21] demonstrated the reconstruction of electrical excitation and active stress from deformation using a simulated deformable excitable medium.…”

Long-Time Prediction of Arrhythmic Cardiac Action Potentials Using Recurrent Neural Networks and Reservoir Computing

“…We expect this goal may necessitate the use of spatially extended models of cardiac tissue as part of the prediction process, although handling the information from spatial neighbors requires very large networks that will pose new computational challenges. The combination of ESNs and local states (Pathak et al, 2018 ; Zimmermann and Parlitz, 2018 ) or specialized deep-learning architectures (Herzog et al, 2018 ) may be useful in tackling such problems, but these methods remain computationally demanding and may require new approaches. In addition, we may need to carefully consider the types of dynamics included in the training data in order to accurately predict transitions between different types of dynamics, such as the transition from normal rhythm to tachycardia or the transition from tachycardia to fibrillation.…”

“…of ESNs and local states (Pathak et al, 2018;Zimmermann and Parlitz, 2018) or specialized deep-learning architectures (Herzog et al, 2018) may be useful in tackling such problems, but these methods remain computationally demanding and may require new approaches. In addition, we may need to carefully consider the types of dynamics included in the training data in order to accurately predict transitions between different types of dynamics, such as the transition from normal rhythm to tachycardia or the transition from tachycardia to fibrillation.…”

EP-Net: Learning Cardiac Electrophysiology Models for Physiology-Based Constraints in Data-Driven Predictions

“…However it suffers from robustness issues in healthcare due to its lack of physiological knowledge. More recently, physics-based learning proposed to use machine learning in order to solve physics equations [9,7,5]. This has the potential to alleviate some numerical and computational time issues, and also to provide a framework to overcome model error.…”