Prediction of excitable wave dynamics using machine learning

Excitable systems can exhibit a variety of dynamics with different complexity, ranging from a single, stable spiral to spiral defect chaos (SDC), during which spiral waves are continuously formed and destroyed. The corresponding reaction-diffusion models, including ones for cardiac tissue, can involve a large number of variables and can be time-consuming to simulate. Here we trained a deep-learning (DL) model using snapshots from a single variable, obtained by simulating a single quasi-periodic spiral wave and SDC using a generic cardiac model. Using the trained DL model, we predicted the dynamics in both cases, using timesteps that are much larger than required for the simulations of the underlying equations. We show that the DL model is able to predict the trajectory of a quasi-periodic spiral wave and that the SDC activation patterns can be predicted for approximately one Lyapunov time. Furthermore, we show that the DL model accurately captures the statistics of termination events in SDC, including the mean termination time. Finally, we show that a DL model trained using a specific domain size is able to replicate termination statistics on larger domains, resulting in significant computational savings.