Go with the Flow: Leveraging Physics-Informed Gradients to Solve Real-World Problems in Water Distribution Systems

Abstract

Clean drinking water is essential for a sustainable society as emphasized by UN’s 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.