1 Introduction
Water loss is a critical global challenge, with leaks in service pipes being particularly difficult to locate due to intermittent flow conditions. Recent sensing work demonstrates that leaks induce specific thermohydraulic signatures—distinct shifts in water temperature (cooling effect due to fresh groundwater) combined with localized upstream flow spikes [2]. However, mapping these signatures to an exact location is an “ill-posed inverse problem” where multiple network scenarios produce similar sensor readings. Purely temporal models (like TCNs) fail to capture the complex spatial topology of physical pipe networks. This thesis proposes a Probabilistic Spatial-Temporal Deep Learning framework using a Physics-Informed Graph Neural Network (GraphSAGE) married to a Neural Spline Flow (NSF) to provide uncertainty-aware, topologically-grounded leak localization.
2 Problem Statement & Objectives
Problem: Current localization methods struggle with ambiguous sensor readings (“Aleatoric Uncertainty”) and often treat the network as a flat collection of sensors, ignoring physical connectivity. Standard models output deterministic single-point predictions, which are risky for excavation planning without confidence intervals.
Objectives:
- Harness real-world dual-channel smart meter data (OptiHyd Temperature and Flow Rate) to maximize the leak signal-to-noise ratio.
- Design a Physics-Informed GraphSAGE Encoder to aggregate spatial-temporal features across the physical pipe network topology.
- Implement a Neural Spline Flow (NSF) decoder to estimate the full, multi-modal probability distribution of the leak location p(y|x) over the network.
- Validate utilizing uncertainty calibration metrics (e.g., 90% CI coverage) and topological error to ensure actionable, reliable “dig zones”.
3 Methodology
3.1 Phase 1: Dual-Channel Data Fusion & Graph Construction
Instead of relying solely on simulated thermal data, this approach leverages real-world smart meter datasets.
- Dual-Channel Features: Processing 24-hour temporal profiles of both water temperature (tracking the thermal anomaly) and flow rate (tracking the hydraulic anomaly).
- Graph Representation: Mapping sensor coordinates and connectivity into a graph adjacency matrix (via exact pipe topologies or K-Nearest Neighbors) to explicitly model spatial dependencies between metering points.
3.2 Phase 2: Architecture (Hybrid GNN + Neural Spline Flow)
The model fundamentally advances standard architectures by combining two powerful paradigms: (1) A GraphSAGE Encoder to process the temporal dual-channel profiles across the spatial graph, allowing nodes to share information with their physical neighbors. (2) A Neural Spline Flow (NSF) Decoder, conditioned on the GNN embeddings, which transforms a simple base distribution into a highly complex, non-linear probability density representing the leak location.
3.3 Comparative Strategy
The proposed hybrid spatial-temporal framework will be evaluated against purely temporal baselines (TCN-NSF) and single-channel configurations.
| Feature | Previous Approach (TCN-NSF) | Proposed (Hybrid GNN-NSF) |
|---|---|---|
| Data Modality | Single-channel (Temperature). | Dual-channel (Temperature + Flow). |
| Spatial Awareness | Blind to physical pipe connections. | Explicitly modeled via Graph Adjacency. |
| Output & Uncertainty | Probability Distribution (NSF). | Probability Distribution (NSF) with higher spatial localized precision. |
| Feature Extraction | Temporal Convolutions (1D-CNN). | Message Passing (GraphSAGE). |
3.4 Phase 3: Evaluation Metrics
- Accuracy & Physics: Mean Absolute Error (MAE) and Topological Error (actual pipe distance in meters) of the median prediction.
- Uncertainty: 90% Confidence Interval (CI) Coverage to verify the reliability of the predicted likelihood maps (“dig zones”).
4 Expected Outcomes
This thesis will demonstrate that pairing Graph Neural Networks with Normalizing Flows, powered by dual-channel thermohydraulic data, drastically outperforms standard methods. It will provide water operators with highly accurate, topologically-aware probability density maps, pinpointing precise excavation zones while mathematically quantifying prediction uncertainty.
5 References
[1] Luis Romero-Ben, Débora Alves, Joaquim Blesa, Gabriela Cembrano, Vicenç Puig, and Eric Duviella. Leak detection and localization in water distribution networks: Review and perspective. Annual Reviews in Control, 55:392–419, 2023.
[2] M. Tolba, M. Ahbab, V. Fehst, H. H. Christensen, A. Maier, and S. Bayer. Leak localization in intermittent-flow pipes using thermohydraulic modeling. In Water Loss 2026, Rio de Janeiro, 2026. IWA Water Loss Specialist Group.