Organizations: SandGold AI Research, China · The Hong Kong University of Science and Technology (Guangzhou), China · Nanyang Technological University, Singapore · Southern University of Science and Technology, China
Deep learning-based super-resolution (SR) can reconstruct fine-scale Earth-observation fields from coarse observations, but reconstruction accuracy alone does not provide a calibrated rule for identifying reliable spatial regions. Conformal Mask Calibration (CMC), built on conformal risk control, converts a spatial uncertainty score into a trust mask and controls the expected worst-case local distortion under exchangeability. However, its fixed threshold can become miscalibrated in Earth-observation streams affected by seasonality and episodic events. We propose CARM (Conformal Adaptive Risk Masking), a statistical framework for adaptive spatial risk control under temporal distribution shift. CARM maintains experts with heterogeneous update rates and aggregates their threshold proposals online using an asymmetric surrogate loss, balancing rapid adaptation to distribution changes against stability during relatively stationary periods. All updates are causal and use only mature feedback available after a fixed delay, allowing CARM to operate with any SR model that provides a spatial uncertainty score. We prove that the time-averaged mask-conditioned risk converges to at most α at an O(1/T) rate, without distributional assumptions and for any choice of aggregation weights across experts. On a daily South China Sea chlorophyll-a SR stream, CARM reduces the empirical violation rate from 43.49% to 9.38% and the moving-average exceedance frequency from 47.29% to 1.22% at α=0.10, while retaining a non-trivial trusted region. Experiments on ERA5 wind and OSTIA sea-surface temperature further show consistent relative improvements across multiple SR backbones.
Figures & tables
Fig. 1: Fixed-step sensitivity on the South China Sea stream at α=0.15 with w=60 . Top: 60-day rolling-loss gap of each fixed-step expert relative to the minimum rolling loss among the experts in each window. Bottom: the adaptation rate η attaining the minimum rolling loss in the corresponding window.
Fig. 2: Overview of CARM. Experts with different step sizes update their threshold proposals. The proposals are aggregated into the deployed threshold τt , which is applied to Ut to generate the trust mask.
α=0.05
α=0.10
α=0.15
Method
Risk ↓
VR (%) ↓
MAER (%) ↓
TS (%)
Risk ↓
VR (%) ↓
MAER (%) ↓
TS (%)
Risk ↓
VR (%) ↓
MAER (%) ↓
TS (%)
CMC
0.0513
47.31
56.11
26.03
0.0989
43.49
47.29
57.51
0.1496
43.40
46.95
94.78
Single expert ( η=0.001 )
0.0354
13.02
5.47
10.14
0.0746
10.42
1.74
42.32
0.1230
16.41
10.76
71.59
Single expert ( η=0.005 )
0.0354
13.02
5.47
10.14
0.0733
9.81
1.65
41.36
0.1191
15.28
9.64
68.42
Single expert ( η=0.020 )
0.0353
13.02
5.47
10.15
0.0728
9.90
1.04
41.04
0.1184
14.24
9.20
68.18
Single expert ( η=0.100 )
0.0354
13.19
5.47
10.27
0.0722
9.46
0.95
40.89
0.1202
14.06
8.59
69.85
TABLE I: Comparison of static CMC, fixed-rate experts, and CARM on the South China Sea Chl-a stream using the FNO backbone. Lower values are preferred for Risk, VR, and MAER, and the best value within each target level is bolded. TS reports retained coverage and is not ranked.
Fig. 3: Temporal risk on the South China Sea stream at α=0.10 . The fixed CMC threshold exhibits sustained near-target or above-target periods under temporal distribution shift, whereas CARM adapts online using matured feedback. The dashed line denotes the target risk level α=0.10 .
Dataset
Backbone
Method
Risk ↓
VR (%) ↓
MAER (%) ↓
Chl-a
FNO
CMC
0.0989
43.49
47.29
CARM
0.0737
9.38
1.22
SRNO
CMC
0.0974
41.24
38.38
CARM
0.0730
10.54
3.32
HiNOTE
CMC
0.1014
43.08
43.29
CARM
0.0736
11.33
6.37
TABLE II: Cross-domain and cross-backbone comparison at α=0.10 .
Fig. 4: Qualitative examples of deployed trust masks on the South China Sea test stream at α=0.10 . Each row corresponds to one representative test sample. From left to right: HR reference, ensemble SR prediction, absolute reconstruction error, and the deployed trust mask. Red regions are rejected as untrusted.
Expert Pool
Risk ↓
VR ↓
MAER ↓
{0.001,0.005}
0.0742
9.90%
1.75%
{0.02,0.1}
0.0727
9.55%
1.05%
{0.001,0.02,0.1}
0.0735
9.64%
1.05%
{0.001,0.005,0.02,0.1}
0.0737
9.38%
1.22%
TABLE III: Effect of expert-pool composition on the South China Sea stream at α=0.10 using the FNO backbone. Lower is better.
α
w
Risk ↓
VR ↓
MAER ↓
0.05
30
0.0366
14.76%
6.28%
60
0.0354
12.93%
5.50%
90
0.0355
13.19%
5.15%
0.10
30
0.0738
10.68%
1.92%
60
0.0737
9.38%
1.22%
90
0.0732
9.46%
1.31%
TABLE IV: Sensitivity to the matured window length on the South China Sea test stream. VR and MAER are reported in percent. Lower is better.
Super-resolution (SR) of satellite imagery is challenging due to the lack of paired low-/high-resolution data. Recent self-supervised SR methods overcome this limitation by exploiting the temporal redundancy in burst observations, but they lack a mechanism to quantify uncertainty in the reconstruction. In this work, we introduce a novel self-supervised loss that allows to estimate uncertainty in image super-resolution without ever accessing the ground-truth high-resolution data. We adopt a decision-theoretic perspective and show that minimizing the corresponding Bayesian risk yields the posterior mean and variance as optimal estimators. We validate our approach on a synthetic SkySat L1B dataset and demonstrate that it produces calibrated uncertainty estimates comparable to supervised methods. Our work bridges self-supervised restoration with uncertainty quantification, making a practical framework for uncertainty-aware image reconstruction.
Zhe Zheng, Valéry Dewil, Pablo Arias
Centre Borelli, ENS Paris-Saclay, Universite Paris-Saclay, CNRS, Gif-sur-Yvette, France · Dept. of Engineering, Universitat Pompeu Fabra, Barcelona, SPAIN
Reliable probability estimates by classifiers are essential in high-risk applications. In practice, however, predicted probabilities are often miscalibrated, and many existing post-hoc calibration methods typically lack guarantees that a specific notion of calibration is achieved after the correction procedure is applied. We introduce a set-based perspective on calibration through the notion of cumulative mass calibration and the corresponding error measures. We propose a new calibration procedure based on conformal prediction that forms cumulative probabilities with guaranteed marginal coverage. We introduce an adaptive temperature scaling algorithm, with the temperature tuned for each input to satisfy the conformal coverage constraint. As we show, this procedure can be efficiently implemented. Across image classification tasks, particularly in settings with many classes, our method improves newly introduced calibration error measures (CMCE and α-CMCE) and standard metrics (such as ECE, cw-ECE, MCE) over the existing baselines.
Daniil Kazantsev, Eric Moulines, Maxim Panov +2
Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, United Arab Emirates · École pour l’informatique et les techniques avancées (EPITA), Paris, France
Super-resolution of geophysical fields presents unique challenges beyond natural image enhancement: fine-scale structures must respect physical dynamics, conserve mass and energy, and evolve coherently in time. These constraints are especially critical for extreme events, where rare, localized, high-intensity features drive impacts and where temporally inconsistent "hallucinated" detail can misrepresent hazards. We introduce CASCADE (Cross-scale Advective Super-resolution with Climate Assimilation and Downscaling Evolution), a framework that reframes spatiotemporal super-resolution as an explicit transport process across scales. Rather than hallucinating high-frequency content per pixel, CASCADE reconstructs fine structure by iteratively advecting coarse information along learned, flow-conditioned velocity fields through semi-Lagrangian warping. The architecture decomposes motion into resolved (large-scale) and subgrid (unresolved) components, mirroring the closure problem in numerical weather prediction, and enforces low-resolution consistency through an assimilation-style innovation step. Evaluated on SEVIR radar data for 4x super-resolution of severe convective storms, CASCADE outperforms strong baselines across both continuous metrics (PSNR, SSIM, MAE) and threshold-based skill scores (CSI, HSS, POD) while providing interpretable diagnostics through visualizable velocity and correction fields. By encoding advection as the fundamental operator rather than learning it implicitly, CASCADE produces temporally coherent, physically consistent, and mass-conserving reconstructions well suited to advection-dominated extremes in atmospheric and oceanic applications.