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Physics-Informed Graph Neural Networks for Water Distribution Systems
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Proposes a physics-informed recursive GCN emulator that estimates heads, flows and demands for water distribution systems with no labeled hydraulic states, trained only on demands and reservoir heads.
Problem
Fast emulation of hydraulic state estimation (heads and flows) in water distribution systems, which EPANET solves slowly and which normally requires extra sensor data for ML surrogates.
Approach
A few GCN layers estimate flows, then a parameter-free message-passing algorithm propagates reservoir heads through the network using hydraulic head-loss equations; both are iterated and trained with an unsupervised loss enforcing consistency between GCN flows, physics-derived flows, and demands.
Key results
- On L-Town Area-C the GCN model emulates in 11.12 s versus 1380.40 s for EPANET (about 124x faster).
- Demand MRAE for the GCN model ranges from 0.324% (Fossolo) to 2.135% (Pescara) across WDS, versus 0.001% to 0.362% for EPANET.
- Head MRAE vs EPANET is at most 0.015% and flow MRAE is 0.295% to 4.663% across the five networks.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace EPANET inference with the physics-informed GCN Model | WDS state estimation · Hanoi | inference time (seconds): 22.87 -> 5.98 seconds | Helped |
| Replace EPANET inference with the physics-informed GCN Model | WDS state estimation · Fossolo | inference time (seconds): 719.86 -> 7.24 seconds | Helped |
| Replace EPANET inference with the physics-informed GCN Model | WDS state estimation · Pescara | inference time (seconds): 1318.86 -> 10.44 seconds | Helped |
| Replace EPANET inference with the physics-informed GCN Model | WDS state estimation · L-Town Area-C | inference time (seconds): 1380.40 -> 11.12 seconds | Helped |
| Replace EPANET inference with the physics-informed GCN Model | WDS state estimation · Zhi Jiang | inference time (seconds): 274.80 -> 15.58 seconds | Helped |
| Replace EPANET demand estimation with the GCN Model | WDS demand estimation · Hanoi, all samples | demand MRAE (%): 0.001 $\pm$ 0.0005 -> 0.179 $\pm$ 0.200 | Hurt |
| Replace EPANET demand estimation with the GCN Model | WDS demand estimation · Fossolo, all samples | demand MRAE (%): 0.115 $\pm$ 0.022 -> 0.324 $\pm$ 0.050 | Hurt |
| Replace EPANET demand estimation with the GCN Model | WDS demand estimation · Pescara, all samples | demand MRAE (%): 0.157 $\pm$ 0.080 -> 2.135 $\pm$ 1.614 | Hurt |
| Replace EPANET demand estimation with the GCN Model | WDS demand estimation · L-Town Area-C, all samples | demand MRAE (%): 0.362 $\pm$ 0.349 -> 1.004 $\pm$ 0.622 | Hurt |
| Replace EPANET demand estimation with the GCN Model | WDS demand estimation · Zhi Jiang, all samples | demand MRAE (%): 0.013 $\pm$ 0.002 -> 0.415 $\pm$ 0.067 | Hurt |
| Include demands reconstructed by the physics-informed algorithm as input node features (ablation) | GCN Model · WDS experiments | performance | No clear effect |
Surprising findings
- Flow estimation errors on a few outlier samples are much larger than demand and head errors, since small erroneous flows do not propagate to equal magnitude errors in demands and heads.
Limitations
- Emulates only demand-driven simulation, not pressure-dependent demand simulation.
- Only tested on pipe-only networks; valves, pumps and tanks are not handled.
- Flow errors on some outlier samples are high; generalization to other WDS structures is not shown.
Experimental setup
Datasets: Hanoi Fossolo Pescara L-Town Area-C Zhi Jiang
Benchmarks: Hanoi Fossolo Pescara L-Town Area-C Zhi Jiang
Metrics: mean relative absolute error (MRAE) inference time (seconds)
Baselines: EPANET
Builds on: EPANET message passing neural networks WNTR
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