DUALFloodGNN

Summary

• DUALFloodGNN is proposed which embeds physical constaints at both global and local scales through explicit loss terms.
• Jointly predicts both nodes and edge features.

Gap it is addressing

• Previous physics-informed GNN implementation enforced mass consevation at global scale only and local mass conservation is implicitly assumed.
• This paper try to address this gap by enforcing both global and node level mass conservation.

Architecture

• Input and outputs

  • static features: area, elevation
  • dynamic features: volume, flow, rainfall, global infow upto p previous timesteps
  • target features: predicts change in water volume $\Delta V$ and water flow $\Delta Q$ from the current timestep to next timestep.

• Encoder

  • 2 encoders for node and edge features. MLP layers.

• Processor: Shared Message Passing

  • $L_{GNN}$ message passing layers
  • Uses MLP to determine messages ($m_{ij}$) for between nodes i and j
  • Aggregation, and fed to MLP to update node embeddings
  • Updated edge embeddings are overwritten with message ($m_{ij}$)
  • Residual connections added at each node

• Decoder

  • Separate decoder for volume and flow
  • MLP layers

Note

The encoders, decoders and message passing functions are all implemented as MLPs with $L_{MLP}$ layers.

• ReLU activation used after each MLP layer.
• Biased term omitted following the design of SWE-GNN.

Physics-informed loss functions

• Multi-task prediction loss: total prediction loss computed as weighted sum of volume (node) and flow (edge) loss.
• Mass balance regularization:
  • Global level regularization: entire catchment considered as control volume
  • Local level regularization: each individual node is considered as control volume

Auto-regressive training

• Multi-step ahead loss: Adopt approach of SWE-GNN.
• Dynamic curriculum learning: First predicting 1-step ahead and then incresaing gradually to target rollout length.

Experimental setup

• Wollombi River watershed in New South Wales, Australia
• 56 flood events simulated using HEC-Residual
• 2D unstructured mesh, graph of 1129 nodes and 2743 edges.
• Each event consistof 576 time steps at 15-mins resolution.

Results

• DUALFloodGNN performed best for both node volume and edge flow prediction
• 2 to 3 orders of magnitude of speed-up compared to numerical solvers
• Water depth RMSE: $0.21\pm 0.07$ m

Important

In contrast to applying only global mass balance, enforcing local-level regularization resulted in a lower RMSE for both node and edge prediction, surpassing the accuracy of the purely data-driven model.