In the context of global warming, extreme events have become more frequent and intense, making their trustworthy detection and forecasting more important than ever. Yet, atmospheric observations lack sufficient spatial resolution, motivating atmospheric data downscaling as a way to reconstruct high-resolution data from coarse observations. This task is now being formulated as a super-resolution (SR) problem with machine learning methods featuring high efficiency. Nevertheless, it remains unclear whether the super-resolved atmospheric data still satisfies fundamental physics governing the Earth system, raising concerns about their trustworthiness in climate-related applications. In this work, we address this challenge by constraining SR models to respect hydrostatic primitive equations that represent multivariate atmospheric physics. First, we propose a Physics-Informed Super-Resolution (PISR) method involving multi-scale physics-informed objectives based on primitive equations. PISR favors the SR outputs to respect these equations and therefore naturally encodes inter-variable relationships. In addition, we propose a metric called Normalized Physical Consistency (NPC) derived from said primitive equations to measure the physical consistency of super-resolved data. Experiments on ERA5, CERRA, and COSMO demonstrate that PISR enhances the reconstruction fidelity by improving physical consistency, SR accuracy, and downstream detection of extreme events, as demonstrated by case studies in heatwaves and extreme winds.
Predicting extreme price movements in high-frequency financial markets is a challenging task due to non-stationarity, heavy-tailed return distributions, and severe class imbalance. In particular, rare but impactful events are often difficult to detect using conventional modeling approaches, which typically treat extreme movements as isolated observations. This study proposes a volatility-aware approach for extreme event detection using high-frequency Bitcoin limit order book (LOB) data. Motivated by empirical evidence of volatility clustering, the target formulation is extended to incorporate both large future returns and high-volatility regimes. This redefinition increases the proportion of informative samples and aligns the learning objective with the underlying market dynamics. Using a tree-based model (XGBoost) with time-series cross-validation and imbalance-aware evaluation, the proposed method achieves a Precision-Recall AUC of approximately 0.40, significantly outperforming the baseline formulation with a PR-AUC of around 0.06. This represents more than a sixfold improvement in detecting rare events. The results highlight that target design plays a critical role in financial machine learning, often exceeding the impact of model complexity. By incorporating volatility structure into the labeling process, the proposed approach provides a more effective and realistic framework for extreme event detection in high-frequency cryptocurrency markets.