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

Researchers have proposed new methods for uncertainty quantification in weather forecasting and regression analysis, addressing a critical gap in current deep learning weather models that produce deterministic forecasts without uncertainty estimates.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but lack uncertainty estimates, according to a study published on arXiv^[1]. The proposed Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) method uses last-layer empirical features and achieves 31--37% sharper prediction intervals at 90% coverage compared to split conformal prediction^[1]. Conformal prediction, a technique used for regression analysis, gives finite-sample coverage guarantees, but most standard constructions are designed for Euclidean output spaces, as noted in another arXiv study^[2]. Adaptive geodesic conformal prediction builds nonconformity scores from geodesic distances, preserving valid marginal coverage and reducing variation in conditional coverage^[2]. The NTK-UQ framework requires no retraining and inference-time uncertainty requires only a single matrix-vector product per sample^[1].