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Spatial-Logic-Aware Weakly Supervised Learning for Flood Mapping on Earth Imagery
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Proposes SLWSL, a neural-symbolic weakly supervised framework that jointly infers high-resolution flood labels from coarse noisy labels using spatial logic rules, EM training, and multi-resolution selective refinement of uncertain cells.
Problem
Flood mapping on high-resolution Earth imagery with only coarse and noisy labels, where physically implausible predictions arise and logic inference over vast pixels is computationally expensive.
Approach
Combines a fine-to-coarse label error model and a spatial-logic-aware label probability model (PSL-style hinge-loss potentials with t-norm fuzzy logic) in a unified likelihood, optimized by EM with a multi-resolution hierarchy that only refines high-uncertainty cells to cut grounding cost.
Key results
- On Dataset 1, SLWSL achieves flood-class F1 of 0.96 versus 0.85 for the Base U-Net and 0.90 for ABL/DPL.
- On Dataset 2, SLWSL achieves accuracy 0.92 versus 0.82 for the Base U-Net.
- Selective refinement grounds 0.78M atoms instead of 4.50M on Dataset 1, giving about 6.31x speedup in the E-step.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add spatial-logic-aware weakly supervised learning | U-Net flood mapping · Dataset 1 | F1 (Flood): 0.90±0.00 -> 0.96±0.00 | Helped |
| add spatial-logic-aware weakly supervised learning | U-Net flood mapping · Dataset 2 | F1 (Flood): 0.86±0.00 -> 0.91±0.01 | Helped |
| add selective refinement during grounding (ablation) | SLWSL · Dataset 1 | F1 (Flood): 0.95±0.00 -> 0.96±0.00 | Helped |
| add selective refinement during grounding (ablation) | SLWSL · Dataset 2 | F1 (Flood): 0.88±0.00 -> 0.91±0.01 | Helped |
| use selective refinement instead of complete grounding (ablation) | SLWSL · Dataset 1 | E-step time (Sec.): 3201 -> 438 | Helped |
| use selective refinement instead of complete grounding (ablation) | SLWSL · Dataset 2 | E-step time (Sec.): 44951 -> 7472 | Helped |
Surprising findings
- Without selective refinement, the full-grounding variant is only slightly less accurate but takes roughly 7x longer to train on Dataset 1 and ~6x on Dataset 2.
Limitations
- Spatial knowledge limited to pre-defined logic rule representations, not graphs, simulations, or PDEs.
- Logical constraints as inductive bias may hinder learning or be misleading if the knowledge base is incomplete or inaccurate.
- Evaluated only on flood data from one hurricane in North Carolina.
Experimental setup
Datasets: North Carolina Hurricane Matthew aerial imagery (NOAA NGS) NC digital elevation imagery (UNC Libraries)
Benchmarks: Hurricane Matthew flood datasets (Dataset 1, Dataset 2)
Metrics: precision recall F1 accuracy
Baselines: Base U-Net U-CAM DeepProbLog Abductive Learning w/o SR variant
Builds on: Probabilistic Soft Logic DeepProbLog Abductive Learning U-Net
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