(388a) Data-Driven Modeling of a Dynamic System with Extreme Events through Neural Networks in an Atlas of Charts

Extreme events in fluid dynamic systems, such as intermittency in turbulence, presents a problem for data-driven modeling. Minute differences in short-time conditions can create vast changes in long-time dynamics, resulting in extreme events occurring with apparently random frequency. Combined with the relative scarcity of extreme events compared to non-extreme states in time series, extreme events tend to be under-forecasted by standard discrete time-mapping neural networks. Our method known as Charts and Atlases for Nonlinear Data-Driven Dynamics on Manifolds, or CANDyMan, overcomes this difficulty 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, obtaining 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 developed by Moehlis, Faisst and Eckhart (MFE), which undergoes extreme events in the form of high-energy, intermittent quasi-relaminarization. We demonstrate that separating the time series into an atlas of charts 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. Additionally, our method exhibits more correct predictions of extreme events, capturing the frequency of high-energy events more accurately than a single neural network. Finally, we project the nine-dimensional predictions onto a full, turbulent velocity field, where our atlas of charts method creates a more accurate reproduction of the actual velocity statistics than a single dynamical model.