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.
Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, United Arab Emirates · École pour l’informatique et les techniques avancées (EPITA), Paris, France