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Physics-Guided Fair Graph Sampling for Water Temperature Prediction in River Networks
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Proposes PGFG, a GraphSAGE-LSTM stream temperature model whose edge sampling is guided by physics-based streamflow-derived influence weights to reduce income- and education-related spatial bias on the Delaware River Basin.
Problem
GNN-based stream water temperature prediction shows substantial performance bias across locations with different income and education levels, which aggregation over neighbors can amplify.
Approach
Defines node influence using physical heat-transfer relations (streamflow-ratio advection terms, multiplied along stream paths) and uses it in an edge modifier that injects/removes neighbors and rescales edge weights to balance influence across sensitive groups, including continuous attributes via density-based candidate selection.
Key results
- PGFG achieves the best discrete-scenario fairness for income (0.134 vs 0.141 DSGNN and 0.157 FairGNN) with RMSE 1.774, comparable to GraphSAGE 1.774.
- For continuous income attribute, PGFG attains worst-case RMSE of 4.456, 3.333, and 2.573 at windows 1000, 3000, 5000, the best among compared methods in the main table.
- For education level continuous scenario, PGFG reduces worst-case RMSE to 3.999, 3.817, 3.597 versus GraphSAGE 4.910, 4.331, 3.959.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use physics-guided influence and fairness-driven edge sampling instead of GraphSAGE | PGFG · Delaware River Basin, income discrete | Fairness: 0.206 -> 0.134 | Helped |
| Use physics-guided influence and fairness-driven edge sampling instead of GraphSAGE | PGFG · Delaware River Basin, education discrete | Fairness: 0.253 -> 0.189 | Helped |
| Use physics-guided influence and fairness-driven edge sampling instead of GraphSAGE | PGFG · Delaware River Basin, income discrete | RMSE: 1.774 -> 1.774 | No clear effect |
| Use physics-guided influence and fairness-driven edge sampling instead of GraphSAGE | PGFG · Delaware River Basin, education discrete | RMSE: 1.774 -> 1.783 | No clear effect |
| Add physical influence weighting rather than balancing only the number of edges (ablation) | PGFG · Delaware River Basin, income discrete | Fairness: 0.196 -> 0.134 | Helped |
| Add physical influence weighting rather than balancing only the number of edges (ablation) | PGFG · Delaware River Basin, income continuous, window 5000 | Worst-case RMSE: 2.901 -> 2.573 | Helped |
| Replace initial adjacency weights with physics-based influence (ablation) | PGFG · Delaware River Basin, income discrete | Fairness: 0.170 -> 0.134 | Helped |
| Replace initial adjacency weights with physics-based influence (ablation) | PGFG · Delaware River Basin, education discrete | Fairness: 0.206 -> 0.189 | Helped |
| Replace initial adjacency weights with physics-based influence (ablation) | PGFG · Delaware River Basin, income continuous, window 5000 | Worst-case RMSE: 2.715 -> 2.573 | Helped |
| Integrate PGFG into the STGNN backbone | STGNN · Delaware River Basin, income discrete | Fairness: 0.196 -> 0.096 | Helped |
Surprising findings
- Balancing only edge counts (FairEdge) or adjacency weights (FairAdj) is insufficient; the physics-based influence is needed for the fairness gains.
- Some fairness-aware methods such as DSGNN attain lower income fairness scores in the continuous scenario but with higher worst-case RMSE than PGFG in several windows.
Limitations
- Evaluated on a single river basin (Delaware River Basin) with two sensitive attributes.
- Relies on PRMS-SNTemp simulated streamflow for most segment-dates (about 70% of data not replaced, only 30% replaced); physical simulation quality affects influence estimates.
- Some low-income and low-education segments still show suboptimal performance due to unmodeled local factors.
Experimental setup
Datasets: Delaware River Basin water temperature observations (USGS NWIS, Water Quality Portal) GridMET meteorological data U.S. Census income and education data PRMS-SNTemp simulated streamflow
Benchmarks: Delaware River Basin stream temperature dataset
Metrics: RMSE fairness disparity (group distance from mean RMSE) worst-case window RMSE
Baselines: GraphSAGE REG FairGNN Bi-Level DSGNN SLDSGNN FairEdge FairAdj STGNN FairFor PGRGrN
Builds on: GraphSAGE FairGNN REG PRMS-SNTemp
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