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Limits to extreme event forecasting in chaotic systems

Yuan YuanAdrian Lozano Duran
Jan 2024
Predicting extreme events in chaotic systems, characterized by rare but intensely fluctuating properties, is of great importance due to their impact on the performance and reliability of a wide range of systems. Some examples include weather forecasting, traffic management, power grid operations, and financial market analysis, to name a few. Methods of increasing sophistication have been developed to forecast events in these systems. However, the boundaries that define the maximum accuracy of forecasting tools are still largely unexplored from a theoretical standpoint. Here, we address the question: What is the minimum possible error in the prediction of extreme events in complex, chaotic systems? We derive lower bounds for the minimum probability of error in extreme event forecasting using the information-theoretic Fano's inequality. The limits obtained are universal, in that they hold regardless of the modeling approach: from traditional linear regressions to sophisticated neural network models. The approach also allows us to assess whether reduced-order models are operating near their theoretical maximum performance or if further improvements are theoretically possible.
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