| Summary: | We develop a framework based on the deep convolutional neural network (DCNN) for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of prediction, a proper labeling scheme can be designated to enable successful training of the DCNN and subsequent prediction of extreme events in time. Given that an extreme event has been predicted to occur within the time horizon, a space-based labeling scheme can be applied to predict, within certain resolution, the location at which the event will occur. We use synthetic data from the two-dimensional complex Ginzburg-Landau equation and empirical wind speed data from the North Atlantic Ocean to demonstrate and validate our machine-learning-based prediction framework. The trade-offs among the prediction horizon, spatial resolution, and accuracy are illustrated, and the detrimental effect of spatially biased occurrence of extreme events on prediction accuracy is discussed. The deep learning framework is viable for predicting extreme events in the real world. © 2022 authors. Published by the American Physical Society.
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