Urban Drainage Network Modeling Based on Physics-Informed Graph Analysis

Urban Drainage Networks (UDNs) are essential for managing flood risks in cities facing intense rainfall, exacerbated by climate change. Many researchers focus on reconstructing and retrofitting UDNs to enhance resilience to urban flooding. Additionally, there is increasing interest in developing real-time flood assessment systems for early warning. These efforts necessitate advanced modeling to accurately measure key hydraulic variables, such as inflow rates and water depths. Conventional tools like the Storm Water Management Model (SWMM) use hydrodynamic simulations but often require extensive calibration and can be computationally intensive. As an alternative, surrogate models provide faster simulations with reasonable accuracy; however, they rely on large datasets and can be case-specific.

This study addresses these research gaps for modeling UDNs by proposing a physics-informed graph network for hydraulic analysis. Unlike traditional surrogate models that derive hydraulic variable data from observed measurements, this framework is fundamentally based on physical laws, such as the conservation of mass and energy. The methodology consists of two main stages. First, the UDN is converted into a directed weighted graph, where nodes represent manholes and edges represent conduits. The edge weights reflect the physical properties of the conduits, helping the model mimic the network's hydraulic behavior. In the second stage, flow routing in the UDN is done using customized graph theory metrics to route the flow within conduits. The flow path from inlet nodes to the network's outfall is determined based on the weighted shortest path principle. Using these flow paths and the pipe capacities, the inflow for each pipe is calculated using a new index called modified runoff edge betweenness centrality.

The developed methodology is applied to two real branched networks in Alpine cities. The physics-informed graph network model was evaluated under 77 rainfall scenarios with varying durations and return periods. The maximum inflow results in the conduits were compared to those obtained by the hydrodynamic model SWMM. The correlation coefficients (R²) ranged from 0.76 to 1 for the first case study and from 0.91 to 1 for the second, demonstrating strong agreement between the surrogate and SWMM models across diverse rainfall scenarios. This physics-informed graph network model is effective in research with limited data and high computational demands, such as real-time UDN assessments and optimization tasks.

Funding: The project “RESTORE” is funded by the Austrian Science Fund (FWF) P 36737-N.