{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:28:32Z","timestamp":1759364912626,"version":"build-2065373602"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032061287","type":"print"},{"value":"9783032061294","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:00:00Z","timestamp":1759363200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T00:00:00Z","timestamp":1759363200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Clean drinking water is essential for a sustainable society as emphasized by UN\u2019s sustainable developmental goal 6. Efficient management of water distribution systems (WDSs) is vital to ensure this goal. Conventional approaches rely on computationally expensive hydraulic simulations. Instead, using a pre-trained physics-informed graph neural network as a surrogate model, we solve such real-world problems with gradient methods. This does not only enable end-to-end optimization of WDS attributes but demonstrates the more general concept of leveraging the differentiability of a deep surrogate model to solve downstream tasks related to the underlying complex system. In this work, we demonstrate this novel principle by focusing on three tasks: First, we estimate hydraulic states from sparse sensory information, achieving SOTA performance. Second, we use the surrogate model combined with information theory to solve the task of optimal sensor placement. We use the sparse-to-dense pressure estimation task to gauge the quality of our sensor placements, which itself is non-trivial. Finally, we plan the rehabilitation of WDSs by optimizing pipe diameters in response to changing demands. To the best of our knowledge, we are the first to use the concept of end-to-end differentiability of complex systems via deep surrogate models to solve real-world tasks in WDSs.<\/jats:p>","DOI":"10.1007\/978-3-032-06129-4_3","type":"book-chapter","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T04:53:14Z","timestamp":1759294394000},"page":"41-59","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Go with\u00a0the\u00a0Flow: Leveraging Physics-Informed Gradients to\u00a0Solve Real-World Problems in\u00a0Water Distribution Systems"],"prefix":"10.1007","author":[{"given":"Inaam","family":"Ashraf","sequence":"first","affiliation":[]},{"given":"Janine","family":"Strotherm","sequence":"additional","affiliation":[]},{"given":"Luca","family":"Hermes","sequence":"additional","affiliation":[]},{"given":"Barbara","family":"Hammer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,2]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Ashraf, I., Hermes, L., Artelt, A., Hammer, B.: Spatial graph convolution neural networks for water distribution systems. In: Advances in Intelligent Data Analysis XXI. Springer (2023)","DOI":"10.1007\/978-3-031-30047-9_3"},{"key":"3_CR2","doi-asserted-by":"crossref","unstructured":"Ashraf, I., Strotherm, J., Hermes, L., Hammer, B.: Physics-informed graph neural networks for water distribution systems. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 38 (2024)","DOI":"10.1609\/aaai.v38i20.30192"},{"key":"3_CR3","doi-asserted-by":"crossref","unstructured":"Babayan, A.V., Savic, D.A., Walters, G.A.: Multi-objective optimization of water distribution system design under uncertain demand and pipe roughness. In: Topics on System Analysis and Integrated Water Resources Management. Elsevier (2007)","DOI":"10.1016\/B978-008044967-8\/50008-7"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Brucherseifer, E., Winter, H., Mentges, A., M\u00fchlh\u00e4user, M., Hellmann, M.: Digital twin conceptual framework for improving critical infrastructure resilience. Automatisierungstechnik 69 (2021)","DOI":"10.1515\/auto-2021-0104"},{"key":"3_CR5","doi-asserted-by":"crossref","unstructured":"Candelieri, A., Ponti, A., Giordani, I., Archetti, F.: Lost in optimization of water distribution systems: better call bayes. Water 14 (2022)","DOI":"10.20944\/preprints202201.0047.v1"},{"key":"3_CR6","doi-asserted-by":"crossref","unstructured":"Creaco, E., Franchini, M., Walski, T.M.: Taking account of uncertainty in demand growth when phasing the construction of a water distribution network. J. Water Resour. Plann. Manag. 141 (2015)","DOI":"10.1061\/(ASCE)WR.1943-5452.0000441"},{"key":"3_CR7","doi-asserted-by":"crossref","unstructured":"Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6 (2002)","DOI":"10.1109\/4235.996017"},{"issue":"3","key":"3_CR8","first-page":"938","volume":"15","author":"W Donath","year":"1972","unstructured":"Donath, W., Hoffman, A.: Algorithms for partitioning graphs and computer logic based on eigenvectors of connection matrices. IBM Tech. Discl. Bull. 15(3), 938\u2013944 (1972)","journal-title":"IBM Tech. Discl. Bull."},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"Ferreira, B., Antunes, A., Carri\u00e7o, N., Covas, D.: Multi-objective optimization of pressure sensor location for burst detection and network calibration. Comput. Chem. Eng. 162 (2022)","DOI":"10.1016\/j.compchemeng.2022.107826"},{"key":"3_CR10","unstructured":"Hajgat\u00f3, G., Gyires-T\u00f3th, B., Pa\u00e1l, G.: Reconstructing nodal pressures in water distribution systems with graph neural networks. arXiv preprint arXiv:2104.13619 (2021)"},{"key":"3_CR11","doi-asserted-by":"crossref","unstructured":"Hu, C., Li, M., Zeng, D., Guo, S.: A survey on sensor placement for contamination detection in water distribution systems. Wirel. Netw. 24 (2018)","DOI":"10.1007\/s11276-016-1358-0"},{"key":"3_CR12","doi-asserted-by":"crossref","unstructured":"Kerimov, B., Taormina, R., Tscheikner-Gratl, F.: Towards transferable metamodels for water distribution systems with edge-based graph neural networks. Water Res. (2024)","DOI":"10.1016\/j.watres.2024.121933"},{"key":"3_CR13","doi-asserted-by":"crossref","unstructured":"Kreuzer, T., Papapetrou, P., Zdravkovic, J.: Artificial intelligence in digital twins\u2013a systematic literature review. Data Knowl. Eng. 151 (2024)","DOI":"10.1016\/j.datak.2024.102304"},{"key":"3_CR14","doi-asserted-by":"crossref","unstructured":"Magini, R., Moretti, M., Boniforti, M.A., Guercio, R.: A machine-learning approach for monitoring water distribution networks (WDNs). Sustainability 15 (2023)","DOI":"10.3390\/su15042981"},{"key":"3_CR15","doi-asserted-by":"crossref","unstructured":"Mala-Jetmarova, H., Sultanova, N., Savic, D.: Lost in optimisation of water distribution systems? A literature review of system design. Water 10 (2018)","DOI":"10.3390\/w10030307"},{"key":"3_CR16","doi-asserted-by":"crossref","unstructured":"Nakka, R., Harursampath, D., Ponnusami, S.A.: A generalised deep learning-based surrogate model for homogenisation utilising material property encoding and physics-based bounds. Sci. Rep. 13 (2023)","DOI":"10.1038\/s41598-023-34823-3"},{"key":"3_CR17","unstructured":"Rossman, L., Woo, H., Tryby, M., Shang, F., Janke, R., Haxton, T.: Epanet 2.2 user\u2019s manual, water infrastructure division. CESER (2020)"},{"key":"3_CR18","doi-asserted-by":"crossref","unstructured":"Santos-Ruiz, I., L\u00f3pez-Estrada, F.R., Puig, V., Valencia-Palomo, G., Hern\u00e1ndez, H.R.: Pressure sensor placement for leak localization in water distribution networks using information theory. Sensors 22 (2022)","DOI":"10.3390\/s22020443"},{"key":"3_CR19","doi-asserted-by":"crossref","unstructured":"Scott, D.W.: Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley (2015)","DOI":"10.1002\/9781118575574"},{"key":"3_CR20","doi-asserted-by":"crossref","unstructured":"Truong, H., Tello, A., Lazovik, A., Degeler, V.: Graph neural networks for pressure estimation in water distribution systems. Water Resour. Res. 60 (2024)","DOI":"10.1029\/2023WR036741"},{"key":"3_CR21","doi-asserted-by":"crossref","unstructured":"Tsiami, L., Makropoulos, C., Savic, D.: Staged design of water distribution networks: a reinforcement learning approach. Eng. Proc. 69 (2024)","DOI":"10.3390\/engproc2024069111"},{"key":"3_CR22","unstructured":"Vrachimis, S., Kyriakou, M., Eliades, D., Polycarpou, M.: Leakdb: a benchmark dataset for leakage diagnosis in water distribution networks description of benchmark. In: Proceedings of WDSA\/CCWI Joint Conference, vol. 1 (2018)"},{"key":"3_CR23","doi-asserted-by":"crossref","unstructured":"Xing, L., Sela, L.: Graph neural networks for state estimation in water distribution systems: application of supervised and semisupervised learning. J. Water Resour. Plann. Manag. 148 (2022)","DOI":"10.1061\/(ASCE)WR.1943-5452.0001550"}],"container-title":["Lecture Notes in Computer Science","Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track and Demo Track"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-06129-4_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T04:53:23Z","timestamp":1759294403000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-06129-4_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,2]]},"ISBN":["9783032061287","9783032061294"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-06129-4_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,2]]},"assertion":[{"value":"2 October 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Porto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ecmlpkdd.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}