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. We propose Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theory 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 consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis (ICA) exploits higher-order statistics to isolate heavy-tailed extreme-event features, beating singular value decomposition (SVD), which captures only second-order variance. A data-driven rule selects ICA or SVD from the feature eigenspectrum, correctly prescribing the superior decomposition for all four evaluated models. Against split conformal prediction, NTK-UQ achieves 31–37% sharper intervals at 90% coverage and uniquely produces adaptive intervals that scale with event severity.

31–37%
sharper intervals than conformal,
at 90% coverage
4
frozen foundation models
(SFNO, Swin Transformer,
Perceiver IO, GNN)
<10 ms
real-time UQ, no retraining,
no extra GPU memory
Method Overview
NTK-UQ pipeline

Figure 1. Atmospheric variables from extreme-weather events pass through a frozen foundation weather model to extract last-layer features. These build the empirical Neural Tangent Kernel, decomposed via SVD or ICA (\(U\Sigma V^\top\)) to a rank-\(k\) approximation. At inference, the GP posterior variance yields calibrated prediction intervals per variable.

NTK-UQ treats a frozen model's last-layer features \(\phi(x)\) as an empirical kernel and returns the Gaussian-process posterior variance per output variable:

\[ K(x, x') = \phi(x)^\top \phi(x'), \qquad \sigma^2(x_*) = \bigl\lVert \tilde{\phi}(x_*) \bigr\rVert^2 + \sigma_n^2 - \sum_{j=1}^{k} \frac{\lambda_j\, c_j^2}{\lambda_j + \sigma_n^2}. \]

Here \(c_j = \tilde{\phi}(x_*)^\top v_j\) projects the centered test feature onto the \(j\)-th kernel eigenvector \(v_j\) (eigenvalue \(\lambda_j\)), and \(\sigma_n^2\) is the noise variance. A post-hoc scale \(\alpha\) calibrates the interval width per variable.

Key Ideas

1. Variance collapse is predictable

When the truncation rank \(k\) approaches the feature space's effective rank, the GP correction term consumes nearly all prior variance and every input looks equally (un)certain. A simple diagnostic ratio \(R_k = C_k/P < 0.9\) flags this before deployment. Concentrated spectra (spectral operators) need aggressive truncation (\(k \le 10\)); attention-based models tolerate full rank.

2. ICA beats SVD on heavy tails

Extreme weather is non-Gaussian and heavy-tailed. SVD captures only second-order variance; ICA exploits higher-order statistics (kurtosis, negentropy) to isolate extreme-event signatures, producing adaptive intervals that SVD cannot recover.

3. A data-driven decomposition rule

The feature eigenspectrum concentration ratio decides the method: concentrated → SVD with low rank, distributed → ICA. This correctly prescribes the superior decomposition for all four evaluated architectures without exhaustive search.

Results

Across 17 variables × 6 lead times × 4 models on a census of 100 EM-DAT extreme-weather events from 2021. Bold marks the decomposition satisfying the 85–95% coverage constraint; conformal prediction is a reference baseline (never highlighted).

ICA vs SVD at optimal rank \(k^*\) (2m temperature)
ModelMethod\(k^*\)CoverageSharpness (\(\sigma\))CRPS
AIFSICA790.6%168.9129.8
AIFSSVD5090.9%144.8133.5
AuroraICA5090.1%602.1701.4
AuroraSVD258.1%11.8935.2
FourCastNetV2ICA389.5%103.261.5
FourCastNetV2SVD189.5%66.364.5
Pangu-WeatherICA4068.4%170620133
Pangu-WeatherSVD4091.1%3552914361

ICA satisfies coverage for 3 of 4 models with lower CRPS; SVD wins only for Pangu-Weather, whose 69-dim pooled features are inherently low-rank.

NTK-UQ vs conformal prediction: mean \(\sigma\) (coverage)
VariableModelLeadNTK-UQ (best)ConformalSharper
2m temp (K)AIFS24h1.98 (91%)2.86 (90%)31%
2m temp (K)FourCastNetV224h1.55 (89%)2.33 (100%)33%
MSL (Pa)AIFS24h524 (91%)776 (95%)32%
MSL (Pa)FourCastNetV224h140 (89%)211 (90%)34%

NTK-UQ achieves lower \(\sigma\) than conformal in 81% of valid comparisons (230/284), at matched \(\approx\)90% coverage.

Adaptivity: coefficient of variation at t+6h (higher = more adaptive)
ModelCV t2m (ICA)CV t2m (SVD)CV msl (ICA)CV msl (SVD)
AIFS0.270.050.270.05
FourCastNetV20.310.060.310.00
Aurora0.090.100.090.10
Pangu-Weather1.81*0.490.090.49

ICA yields ~5× higher CV than SVD for AIFS and FourCastNetV2, i.e. intervals that scale with event severity. *Pangu-ICA is excluded (68.4% coverage).

Spatial Uncertainty
AIFS spatial uncertainty for Typhoon Odette

Figure 2. AIFS spatial uncertainty for Typhoon Odette (2021-12-16, Philippines), t+12h. The NTK-UQ uncertainty map (right) concentrates near the cyclone track, aligning with forecast error to enable targeted warnings for landfall zones rather than uniform domain-wide alerts.

Citation
@inproceedings{minoza2026ntkuq,
  author    = {Mi\~noza, Jose Marie Antonio and Laylo, Rex Gregor and Iba\~nez, Sebastian C.},
  title     = {Scalable Uncertainty Quantification for Extreme Weather
               Forecasting via Empirical Neural Tangent Kernels},
  booktitle = {Proceedings of the 32nd ACM SIGKDD Conference on Knowledge
               Discovery and Data Mining (KDD '26)},
  year      = {2026},
  doi       = {10.1145/3770855.3818106}
}