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

TL;DR

This paper introduces CANDyMan, a data-driven method that decomposes turbulent flow data into charts to improve the prediction of rare and extreme events in complex dynamical systems.

Contribution

The paper applies the CANDyMan technique to turbulent shear flow data, demonstrating improved forecasting of extreme events over traditional neural network models.

Findings

Enhanced prediction accuracy of extreme events.

Better estimation of time until laminarization.

More reliable long-term forecasts of turbulent dynamics.

Abstract

Dynamical systems with extreme events are difficult to capture with data-driven modeling, due to the relative scarcity of data within extreme events compared to the typical dynamics of the system, and the strong dependence of the long-time occurrence of extreme events on short-time conditions.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 $\textit{Charts and Atlases for Nonlinear Data-Driven Dynamics on Manifolds}$, or CANDyMan, overcomes these difficulties by decomposing the time series into separate charts based on data similarity, learning dynamical models on each chart via individual time-mapping neural networks, then stitching the charts together to create a single atlas to yield a global dynamical model. We apply CANDyMan to a nine-dimensional model of turbulent shear flow between infinite parallel free-slip walls under a sinusoidal body force [Moehlis, J., Faisst, H. & Eckhardt, B. A low-dimensional model for turbulent shear flows. New J Phys $\textbf{6}$, 56 (2004)], which undergoes extreme events in the form of intermittent quasi-laminarization and long-time full laminarization. We demonstrate that the CANDyMan method allows the trained dynamical models to more accurately forecast the evolution of the model coefficients, reducing the error in the predictions as the model evolves forward in time. The technique exhibits more accurate predictions of extreme events, capturing the frequency of quasi-laminarization events and predicting the time until full laminarization more accurately than a single neural network.