Prediction of dragon king extreme events using machine learning approaches and its characterizations

In this study, we employ a machine learning approach to infer the complex dynamics of dragon king extreme events. Specifically, we utilize two distinct machine learning techniques: Echo State Network and Gated Recurrent Unit. To do so, we consider three distinct systems for predicting dragon kings behavior: a pair of electronic circuits, coupled logistic maps, and Hindmarsh-Rose neurons. We discover that a few actual time series data points, accompanied by their corresponding system parameters, are adequate to capture dragon kings nature. Initially, we demonstrate that systems under consideration possess characteristics of extreme events, with signal amplitudes greater than the critical amplitude threshold. The presence of dragon kings within these observed extreme events is discerned by the emergence of hump-like behavior in the tail distribution of the probability density function and the statistical measures. Finally, we calculate the root mean square error to determine the accuracy of the predicted dynamics.