Identifying spiral wave tips with reservoir computing

Identifying spiral wave tips of spatiotemporal dynamical systems from time series represents a significant challenge for understanding and controlling complex dynamics. Many previous methods for calculating tips relied on phase analysis, and they inevitably needed to set a phase origin and required multiple time slices for phase calculation. Reservoir computing, a simplified recurrent neural network paradigm, has spurred many investigations in several fields to capture and predict the features of complex, nonlinear dynamics. Based on the superior performance of reservoir computing, we investigated its application in analyzing spiral wave tips in reaction–diffusion systems. In this paper, we employ reservoir computing to identify spiral wave tips in some simple cases (spiral waves modeled by CGLE with one or two tips) and demonstrated that our model could accurately identify tips using only one time slice. Furthermore, we confirmed that the model maintained high accuracy in identifying tips of moving one-tip spiral waves in other systems (Bär, FHN). Moreover, we analyzed complex cases (evolving spiral waves and turbulence), with results indicating effective model performance. Ultimately, we demonstrated reservoir computing’s robustness, noting its superior performance over conventional algorithms when handling data contaminated with noise from the sampling process. In summary, reservoir computing exhibits low computational complexity, requires minimal data and fewer constraints, and achieves high accuracy. This approach offers novel prospects for identifying topological structures in practical applications, such as monitoring and controlling spiral wave tips in cardiac illnesses.