Sensor Placement in Water Distribution Networks using Graph Neural Networks

Graph Neural networks have shown the potential to solve large-scale combinatorial optimisation problems. The following work demonstrates how the graph neural networks can be utilised to solve the sensor placement problem, a combinatorial optimisation problem. This paper focuses on the problem of placing pressure sensors optimally in a Water Distribution Network (WDN). The problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) or Ising model, a combinatorial optimisation problem. The paper outlines the QUBO and Ising formulations for the sensor placement problem, starting from the network topology and other relevant features. A detailed procedure is presented for solving the problem by minimising its Hamiltonian using PyQUBO, an open-source Python Library. Finally, the proposed methods are applied to a real Water Distribution Network for evaluation.