Scalable Uncertainty Quantification for Extreme Weather Forecasting via Empirical Neural Tangent Kernels

2026-06-01

AI Summary

This work addresses the critical limitation of existing deep learning weather forecasting models—their lack of reliable uncertainty quantification, which hinders high-stakes decision-making during extreme weather events. Leveraging the neural tangent kernel (NTK) framework, the authors introduce a Gaussian process correction term constructed from empirical features of the final network layer, enabling inference-time uncertainty estimation without model retraining. By uncovering an architecture-dependent variance collapse mechanism, they propose a data-driven decomposition strategy based on the spectral concentration of features, which for the first time yields prediction intervals that adapt to the severity of extreme events. At 90% coverage, the resulting intervals achieve 31–37% improved sharpness over split conformal prediction.

Abstract

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.

Problem

• Uncertainty Quantification
• Extreme Weather Forecasting
• Deep Learning
• Neural Tangent Kernel
• Prediction Intervals

Innovation

• Neural Tangent Kernel
• Uncertainty Quantification
• Extreme Weather Forecasting
• Independent Component Analysis
• Adaptive Prediction Intervals