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已达到与数值天气预报相当的精度，同时运行速度快数个数量级，但这些模型仅生成确定性预报，缺乏不确定性估计——这在极端天气事件的高风险决策中构成关键缺陷。本文提出基于神经切向核的不确定性量化方法（NTK-UQ），利用最后一层经验特征实现量化。理论分析表明，不确定性量化质量通过两种机制依赖于架构：第一，方差坍缩机制揭示了不确定性量化失效的条件——当特征值截断秩逼近特征空间的有效秩时，高斯过程修正项消耗几乎所有先验方差，导致热带气旋与常规天气的区分能力丧失；谱集中型架构（谱算子）需激进截断（k ≤ 10），而注意力机制模型可容忍满秩计算。第二，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）分离极端事件的重尾特征，相较仅捕获二阶方差的奇异值分解获得更高区分度。基于特征特征谱集中比率的数据驱动选择规则，可正确为全部四种评估架构指定最优分解方法。与分裂共形预测（天然后验基线）相比，NTK-UQ在90%覆盖率下预测区间缩窄31-37%，且独特地生成与极端事件严重程度成比例的自适应区间——这是共形预测架构性无法实现的。本框架无需重新训练；推理时不确定性仅需每个样本计算一次矩阵-向量乘积。