A numerical method for coupling parameterized physics-informed neural networks and FDM for advanced thermal-hydraulic system simulation

Severe accident analysis with system codes such as MELCOR is indispensable for nuclear safety assessment, yet the cost of repeated simulations constrains parametric studies and uncertainty quantification. Data-driven surrogates accelerate these analyses but require large simulation datasets, whereas physics-informed neural networks (PINNs) require no training data yet must be retrained for every parameter change and lose accuracy over long horizons. This study addresses both limitations with the P2F method — Parameterized PINNs coupled with the finite difference method (FDM) — for MELCOR’s Control Volume Hydrodynamics/Flow Path (CVH/FL) module. A parameterized Node-Assigned PINN (NA-PINN) takes the water-level difference, initial velocity, and time as inputs, learning a solution manifold so that a single trained network serves as a data-free surrogate for the momentum equation at all flow paths. The parameterized NA-PINN is coupled with an FDM solver that advances the mass conservation equation at each time step, conserving mass exactly in the discrete sense while replacing the iterative nonlinear momentum solution with a single forward pass. Because the network is evaluated only within one time step and re-anchored to the FDM-updated state, the long-horizon training limitation is avoided. For a six-tank gravity-driven draining scenario, the water-level mean absolute error was 9 . 3 2 × 1 ⁢ 0 − 5 m and the velocity error 3 . 0 8 × 1 ⁢ 0 − 3 m/s at 𝛥 ⁢ 𝑡 = 1 . 0 s. This accuracy holds for time steps from 0.2 to 1.0 s and five initial conditions without retraining or data. To the best of the authors’ knowledge, this is the first data-free parameterized PINN coupled with an FDM solver for thermal-hydraulic system-code modeling.