Prediction of excitable wave dynamics using machine learning.

Area of Science:

• Computational biology
• Nonlinear dynamics
• Artificial intelligence

Background:

• Excitable systems display complex dynamics, from stable spiral waves to spiral defect chaos (SDC).
• Simulating these systems, particularly cardiac tissue models, is computationally intensive due to numerous variables and small timesteps.
• Current models struggle with the rapid formation and destruction of spiral waves in SDC.

Purpose of the Study:

• To develop a deep learning (DL) model for predicting dynamics in excitable systems.
• To reduce the computational cost of simulating complex wave phenomena like SDC.
• To assess the accuracy of DL predictions for spiral wave trajectories and SDC termination statistics.

Main Methods:

• Trained a DL model using simulation snapshots of a single variable from a generic cardiac model.
• Used data from both quasi-periodic spiral wave dynamics and SDC.
• Employed significantly larger timesteps for DL predictions compared to traditional simulations.

Main Results:

• The DL model accurately predicted the trajectory of quasi-periodic spiral waves.
• SDC activation patterns were predicted for approximately one Lyapunov time.
• The DL model accurately captured SDC termination event statistics, including mean termination time.
• A DL model trained on a specific domain size successfully replicated termination statistics on larger domains.

Conclusions:

• Deep learning offers a computationally efficient method for simulating complex dynamics in excitable systems.
• DL models can accurately predict wave propagation and chaotic dynamics, including termination events.
• DL models trained on smaller domains can generalize to larger ones, demonstrating significant computational savings and potential for complex system modeling.