Coupling a parameterized PINN with FDM by node assignment yields water-level MAE of about 7.85×10⁻⁵ m and velocity MAE of about 3.21×10⁻³ m/s in a six-tank draining case without retraining
This study develops the P2F method, a node-assigned hybrid framework that couples a parameterized Node-Assigned physics-informed neural network (NA-PINN) with a finite difference method (FDM) solver: the parameterized NA-PINN takes the water-level difference, initial velocity, and time t as inputs and learns a solution manifold so that a single trained network serves as a data-free surrogate for the momentum conservation equation across all flow paths, while the FDM solver advances the mass conservation equation at each time step to ensure exact discrete mass conservation; verification on a six-tank gravity-driven draining scenario yields a water level mean absolute error of 7.85×10⁻⁵ m and a velocity mean absolute error of 3.21×10⁻³ m/s under the nominal condition with Δt = 1.