Extreme Event Aware ($η$-) Learning

2025-10-21

AI Summary

Modeling and predicting extreme events in complex dynamical systems is hindered by severe scarcity of extreme-event data. Method: We propose a novel deep learning framework that requires no historical extreme samples. It introduces a quantifiable observability metric for extremeness, whose statistical properties inform a regularization term; integrates optimal transport theory to ensure extrapolation optimality; and leverages unlabeled data to implicitly learn the distribution of extreme regions. Contribution/Results: The framework enables low-uncertainty modeling and generation of previously unseen extreme scenarios. Evaluated on multiple prototypical dynamical systems and a real-world precipitation downscaling task, it significantly reduces epistemic uncertainty in extreme regimes, successfully generates extreme events absent from training, and improves predictive robustness and generalization.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Quantifying and predicting rare and extreme events persists as a crucial yet challenging task in understanding complex dynamical systems. 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 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 `uncharted' extreme event regions, by enforcing the extreme event statistics of an observable indicative of extremeness during training, which can be available through qualitative arguments or estimated with unlabeled data. This type of statistical regularization results in models that fit the observed data, while enforcing consistency with the prescribed observable statistics, 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 $η$-learning framework on several prototype problems and real-world precipitation downscaling problems.

Problem

• Quantifying rare extreme events in complex dynamical systems
• Overcoming high uncertainty in data-scarce extreme regions
• Generating unprecedented extremes without training data examples

Innovation

• Uses statistical regularization without extreme event data
• Enforces observable statistics for extreme event prediction
• Applies optimal transport theory for method justification