Predicting extreme events by identifying precursors on the chaotic attractor manifold

Predicting spatiotemporal extreme events using dynamical systems theory poses several major challenges. One of these is the phase space dimensionality of spatiotemporal systems. Extreme events are rare, while the number of variables that could potentially drive them is large. Often, a subset of the phase space is sampled, or features are engineered based on previous research on drivers, to predict spatiotemporal extreme events. On the other hand, the background attractors are often assumed to be of much smaller dimensionality than the phase space. Therefore, we propose a novel framework that approximates the background attractor of chaotic systems using an autoencoder. On this lower-dimensional attractor representation, precursor densities are created from historical analogues. Based on these precursor densities, predictions of extreme events are made. This framework proves to be efficient in predicting extreme events in a simplified turbulent flow and a climate model. Without engineering-specific predictor feature sets, this lower-dimensional representation of the attractor allows for more efficient and accurate analog prediction of extreme events in large chaotic systems.