Author(s): Shixun Li; Wenchong Tian; Hexiang Yan

Linked Author(s):

Keywords: Pproximate Riemann solver; Hydrodynamic simulator; Physics-based deep learning; Saint Venant Equations; Transient mixed flow

Abstract: The current research explores the application of physics-informed neural networks (PINN) in solving the Saint-Venant equations (SVE) for transient mixed flow in urban drainage network systems. This paper firstly defines a coefficient to unify water hammer and open channel equations into SVE, and then embedded it into the loss function in the neural networks. Meanwhile, the water height, velocity, and this coefficient can be outputted in three sub-networks separately with different network-architecture and hyperparameters. And the training dataset is obtained from physical experiments, while the test dataset is based on a numerical solution using finite volume Harten-Lax-van Leer (HLL) solver. By embedding governing equations as the loss function, setting the initial conditions, boundary conditions, and data from experimental monitoring gauges, this surrogate model can directly solve for water depth (or pressure) and velocity within the corresponding computational domain by inputting temporal and spatial information. Ultimately, a sensitivity analysis was undertaken concerning hyperparameter selection, with subsequent discourse on the limitations inherent to PINN.

DOI: https://doi.org/10.3850/iahr-hic2483430201-301

Year: 2024