Predictability of Extreme Events : Data-driven Modeling in the Complex Systems Framework

Extreme events are inherent elements of fluctuations in natural and anthropogenic systems and quantifying their predictability has been a long-standing challenge. The data-driven modeling and prediction in the complex systems framework provides a trans-disciplinary approach to quantifying predictability of extreme events and associated natural hazards. The difficulties arising from the low-probability high-impact nature of extremes require detailed and reliable characterization of the variability of the system. An approach that brings together the dynamical systems analysis with the fluctuation analysis in a self-consistent manner yields predictions of the events and their associated probabilities. This approach in the complex systems framework integrates the data-driven modeling of dynamics from time-series data, scaling behavior of fluctuations in nonequilibrium systems, and characterization of heavy-tail distributions from scaling indices. The dynamical features derived from the time series data using the time-delay embedding technique of dynamical systems yield predictions of the typical or mean-field behavior inherent in the system and is used to define the fluctuations. This provides a self-consistent method for defining fluctuations and thus overcomes the arbitrariness inherent in the widely used detrended fluctuation analysis techniques. The large deviations from the mean-field trend are the extreme events and their key feature is the presence of long-range correlation in the system, characterized by scaling indices. The relationship between scaling indices and heavy-tails in the distribution functions, based on the limit theorems for such systems, yields a means for computing the probabilities of extreme events. Further, this approach provides a comprehensive framework for quantifying predictability of extreme events by integrating machine learning and complex systems approaches. A combination of the dynamical systems modeling with the long-short-term memory recurrent neural network in space weather provides an example. The random forest model in ensemble learning incorporated in the dynamical model yields improvements in the mean-field predictions, and examples from space weather will be presented.