无需极端数据也能预测极端事件，提升模型在未知极端场景的可靠性。
Extreme Event Aware ($η$-) Learning
- 通过统计约束引导训练，利用可观测极值特征增强模型泛化能力。
- 在无极端样本情况下仍能生成前所未有的极端事件，且不确定性显著降低。
- 适合气候模拟、灾害预警等极端事件预测场景，尤其数据稀缺时。
量化与预测罕见且极端事件极具挑战，因其发生频率低、影响严重且模拟成本高。现有数据驱动方法通常需训练数据中包含多个极端事件，导致平静状态预测准确但极端区域存在高认知不确定性。为此，本文提出极端事件感知（η-）学习，无需极端事件出现在可用数据中。该方法在训练中强制施加由定性知识或无标签数据获取的极值可观测量的统计特性，从而在拟合观测数据的同时保持与预设统计的一致性，实现对前所未有极端事件的生成。基于最优传输的理论结果提供了严格依据并确立关键最优性性质。原型系统及真实降水降尺度问题的数值实验验证了η-学习框架的有效性。
原文摘要 · Abstract (English)
Quantifying and predicting rare and extreme events is challenging because such events are infrequent, severe, and expensive to simulate. Existing data-driven methods often require multiple extremes in the training data or sampling process, leading to accurate predictions in quiescent regimes but high epistemic uncertainty in extreme-event regions. To overcome this limitation, we introduce Extreme Event Aware ($η$-) Learning, which does not require extreme events in the available data. The method reduces uncertainty even in uncharted extreme regimes by enforcing during training the statistics of an observable indicative of extremeness, obtained from qualitative knowledge or unlabeled data. This statistical regularization results in models that fit observed data while remaining consistent with prescribed observable statistics, enabling the generation of unprecedented extreme events. Optimal-transport-based theoretical results offer rigorous justification and establish key optimality properties. Numerical experiments on prototype systems and real-world precipitation downscaling problems demonstrate the effectiveness of the $η$-learning framework.
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