p-Laplacian based surrogate modeling of water distribution systems

Mario Putti

Department of Agronomy, Food, Natural resources And Environment, UniPD

Thursday 27th February 2025

14:00:00

Aula Saleri

Precise modeling of an operational Water Distribution System (WDS) is a non-trivial and intricate task. Indeed, many of the hydraulic characteristics of the original WDS components (pipes and valves) may drastically change in time due in particular to aging. For this reason, the original model used in the design phase is unrealistic and a new parameter set needs to be calibrated for each WDS component. Because of the complexity of the system and the consequential difficulty in the determination of the actual values of the hydraulic parameters, the development of accurate operational models is inaccessible for real scale aqueducts. In this work we propose a surrogate model of a WDS based on a weighted p-Laplace operator defined on the graph representing the aqueduct. In other words, we postulate the existence of appropriate distributions of spatially varying weights and exponents such that the solution of the corresponding weighted p-Poisson equation with the water demand as forcing function actually describes the behavior of the WDS. Thus, we formulate a TV-regularized p-Calderon inverse problem to identify the weight and exponent distributions and formulate a gradient flow scheme for its numerical solution. A complex real aqueduct characterized by 138 km of pipes is used to verify the applicability of the proposed surrogate model and assess its accuracy in reproducing the real behavior. Contatti: alessio.fumagalli@polimi.it