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README.md

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-license: isc
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+# Factor Graph Optimization for Leak Localization in Water Distribution Networks
+
+![Factor Graph for Leak Localization](figures/fgo-design.png?raw=true)
+
+Implementation and [experimental data](network_data) for the [paper](https://arxiv.org/pdf/2509.10982)
+
+> P. Irofti, L. Romero-Ben, F. Stoican, and V. Puig,
+“Factor Graph Optimization for Leak Localization in Water
+Distribution Networks,"
+pp. 1--12, 2025.
+
+If you use our work in your research, please cite as:
+```
+@article{IRSP25_fgll,
+  author = {Irofti, P. and Romero-Ben, L. and Stoican, F. and Puig, V.},
+  title = {Factor Graph Optimization for Leak Localization in Water
+Distribution Networks},
+  year = {2025},
+  pages = {1-12},
+  eprint = {2509.10982},
+  archiveprefix = {arXiv},
+}
+```
+
+## Prerequisite
+Before running make sure you have installed the Python packages:
+* [numpy](https://numpy.org/)
+* [scipy](https://scipy.org/)
+* [gtsam](https://gtsam.org/)
+* [wntr](https://github.com/USEPA/WNTR)
+
+## Usage
+Run [test_FGLL.py](test_FGLL.py) and set the network parameter to `Modena`, `LTOWN` or `toy_example`. Default is `Modena`.
+
+## Description
+Detecting and localizing leaks in water distribution network systems is an important topic with direct environmental, economic, and social impact.
+Our paper is the first to explore the use of factor graph optimization techniques for leak localization in water distribution networks,
+enabling us to perform sensor fusion between pressure and demand sensor readings
+and to estimate the network's temporal and structural state evolution across all network nodes.
+The methodology introduces specific water network factors and proposes a new architecture composed of two factor graphs:
+a leak-free state estimation factor graph and a leak localization factor graph.
+When a new sensor reading is obtained,
+unlike Kalman and other interpolation-based methods,
+which estimate only the current network state,
+factor graphs update both current and past states.
+Results on Modena, L-TOWN and synthetic networks show that factor graphs are much faster than nonlinear Kalman-based alternatives such as the UKF,
+while also providing improvements in localization compared to state-of-the-art estimation-localization approaches.
+
+## Contents
+1. The **Factor Graph Leak Localization** (FGLL) algorithm is in [FGLL.py](FGLL.py).
+
+2. The custom **water factors** are in [water_factors.py](water_factors.py).
+
+3. Specific water distribution network data are in [network_data](network_data).
+
+## Results
+
+In the paper we compared our results with [GHR-S](https://www.sciencedirect.com/science/article/abs/pii/S0043135423001823?via%3Dihub), [GSI](https://github.com/luisromeroben/PhD/tree/master/Chapter3) and [UKF-AW-GSI](https://github.com/luisromeroben/D-UKF-AW-GSI).
+
+![Normalized leak metric for each potential leak](figures/matrix_tile_texample.png?raw=true)
+
+Description: Normalized leak metric for each potential leak, comparing GHR-S, GSI, UKF-AW-GSI and FGLL. Each image encodes a colour code of the normalized metric of a node (x-axis) in a leak scenario (y-axis).