Title: Prediction of excitable wave dynamics using machine learning Show Chinese title

Title: 利用机器学习预测可激发波动力学

Abstract: 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 activaton 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. Show Chinese abstract

Abstract: 兴奋性系统可以表现出各种复杂程度不同的动力学行为，从单一的稳定螺旋到螺旋缺陷混沌（SDC），在此期间螺旋波不断形成和消失。 对应的反应-扩散模型，包括心脏组织的模型，可能涉及大量变量，并且模拟起来可能非常耗时。 在这里，我们利用由通用心脏模型模拟单个准周期螺旋波和SDC所获得的单变量快照训练了一个深度学习（DL）模型。 使用训练好的DL模型，我们以远大于求解基础方程模拟所需的步长来预测这两种情况的动力学。 我们展示了DL模型能够预测准周期螺旋波的轨迹，并且可以预测大约一个李雅普诺夫时间内的SDC激活模式。 此外，我们展示DL模型准确捕捉了SDC终止事件的统计特性，包括平均终止时间。 最后，我们展示了使用特定域大小训练的DL模型能够在更大域上复制终止统计数据，从而实现显著的计算节省。