Generating Unprecedented Extreme Scenarios with Limited Data

Abstract

Quantifying and predicting rare and extreme events persists as a crucial yet challenging task in understanding complex dynamical systems, ubiquitous in science and engineering. Many practical challenges arise from the infrequency and severity of these events, including the considerable variance of simple sampling methods and the substantial computational cost of high-fidelity numerical simulations. Numerous data-driven methods have recently been developed to tackle these challenges. However, a typical assumption for the success of these methods is the occurrence of multiple extreme events, either within the training dataset or during the sampling process. This leads to accurate models in regions of quiescent events but with high epistemic uncertainty in regions associated with extremes. To overcome this limitation, we introduce the framework of Extreme Event Aware (e2a or eta) or η-learning which does not assume the existence of extreme events in the available data. η-learning reduces the uncertainty even in ‘unchartered’ extreme event regions, by enforcing the extreme event statistics of a few observables during training, which can be available or assumed through qualitative arguments or other forms of analysis. This type of statistical regularization results in models that fit the observed data, but also enforces consistency with the prescribed statistics of some observables, enabling the generation of unprecedented extreme events even when the training data lack extremes therein. Theoretical results based on optimal transport offer a rigorous justification and highlight the optimality of the introduced method. Additionally, extensive numerical experiments illustrate the favorable properties of the ηlearning framework on several prototype problems and real-world precipitation downscaling problems.