Modeling transient mixed flows in sewer systems with data fusion via physics-informed machine learning

Transitions between free-surface and pressurized flows, known as transient mixed flows, have posed significant challenges in urban drainage systems (UDS), e.g., pipe bursts, road collapses, and geysers. However, traditional mechanistic modeling for mixed flows is challenged by the difficult integration of multi-source data, complex equation forms for the discovery of dynamic processes, and high computational demands. In response, we proposed a data-driven model, TMF-PINN, which utilizes a Physics-Informed Neural Network (PINN) to simulate and invert Transient Mixed Flow (TMF) in sewer networks. This model integrates experimental data, simulation results and Partial Differential Equations (PDEs) into its loss function, leveraging the extensive data available in smart urban water systems. A status factor (α) has been introduced to seamlessly link open channel and pressurized flow dynamics, facilitating rapid adjustments in wave speed. On this basis, Fourier feature extraction and quadratic neural networks have been employed to capture complex dynamic processes featuring high-frequency. Validation through three classical cases using the Storm Water Management Model (SWMM) and comparisons with finite volume Harten-Lax-van Leer (HLL) solver reveal that the proposed model circumvents the constraints of spatiotemporal resolution, yielding accurate flow field predictions.