2022 Annual Meeting
Utilizing the Euler Characteristic for Extreme Event Detection
Predicting extreme events in complex systems can be critical to understanding dynamics in fields such as weather. Many existing methods for extreme event prediction require careful work in identifying the relevant predictors and require abundant training data. Current methods use convolutional neural networks, maximally divergent intervals, and connected regions in topological space. Topology provides a range of mathematical tools used to characterize shapes within space. By using the Euler characteristic (EC), which capitalizes on the fact that there are topological changes in many systems prior to extreme events, we overcome the challenges in these approaches. The EC is a topological data analysis tool used to analyze complex systems relating to extreme weather event detection. The EC methodology proves to be ideal for dimensionality reduction, visualization, and classification. Projecting onto only a few principal components of the EC leads to a clear separation of extreme events. We validate this method on Kolmogorov flow and geophysical data and how we can outperform other methods of predicting when extreme events will happen.