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Dynamical systems with extreme events are difficult to capture withdata-driven modeling, due to the relative scarcity of data within extremeevents compared to the typical dynamics of the system, and the strongdependence of the long-time occurrence of extreme events on short-timeconditions.A recently developed technique [Floryan, D. & Graham, M. D.Data-driven discovery of intrinsic dynamics. Nat Mach Intell $\textbf{4}$,1113-1120 (2022)], here denoted as $\textit{Charts and Atlases for NonlinearData-Driven Dynamics on Manifolds}$, or CANDyMan, overcomes these difficultiesby decomposing the time series into separate charts based on data similarity,learning dynamical models on each chart via individual time-mapping neuralnetworks, then stitching the charts together to create a single atlas to yielda global dynamical model. We apply CANDyMan to a nine-dimensional model ofturbulent shear flow between infinite parallel free-slip walls under asinusoidal body force [Moehlis, J., Faisst, H. & Eckhardt, B. A low-dimensionalmodel for turbulent shear flows. New J Phys $\textbf{6}$, 56 (2004)], whichundergoes extreme events in the form of intermittent quasi-laminarization andlong-time full laminarization. We demonstrate that the CANDyMan method allowsthe trained dynamical models to more accurately forecast the evolution of themodel coefficients, reducing the error in the predictions as the model evolvesforward in time. The technique exhibits more accurate predictions of extremeevents, capturing the frequency of quasi-laminarization events and predictingthe time until full laminarization more accurately than a single neuralnetwork.

Predicting extreme events in a data-driven model of turbulent shear flow using an atlas of charts