Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation ($k \leq 10$), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37\% sharper prediction intervals at 90\% coverage, and uniquely produces \emph{adaptive} intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

翻译：深度学习天气模型现在能够达到数值天气预报的精度，同时运行速度快出数个数量级，但其生成确定性预报而缺乏不确定性估计，这在极端天气事件的高风险决策中是一个关键缺陷。本文提出一种基于神经正切核的不确定性量化方法（NTK-UQ），利用最后一层经验特征。理论分析预测，不确定性量化质量通过两种机制依赖于架构。首先，一种方差崩溃机制解释了不确定性量化何时失效：当特征值截断秩接近特征空间的有效秩时，高斯过程校正项消耗几乎所有先验方差，破坏了热带气旋与常规条件之间的区分能力；具有集中谱（谱算子）的架构需要激进截断（k ≤ 10），而基于注意力的模型可容忍全秩计算。其次，分解性能取决于极端天气的非高斯、重尾结构：独立成分分析利用高阶统计量（峰度、负熵）来分离重尾极端事件特征，相比仅捕获二阶方差的奇异值分解，实现了更高的区分度。一种数据驱动的选择规则根据特征谱集中比率来选择独立成分分析或奇异值分解，对所有四种评估架构正确指定了更优的分解方法。与分割共形预测（自然的事后基线）相比，NTK-UQ在90%覆盖率下实现了31-37%更窄的预测区间，并且独特地生成了随极端事件严重性缩放的自适应区间，而共形预测从构造上无法实现这一点。该框架无需重新训练；推理时的不确定性仅需每个样本进行一次矩阵-向量乘积运算。