A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation

TL;DR

This paper introduces a hybrid numerical framework combining parameterized physics-informed neural networks with finite difference methods to efficiently simulate thermal-hydraulic systems, reducing computational costs and avoiding retraining.

Contribution

The study develops a novel parameterized PINN coupled with FDM framework that generalizes across parameters and initial conditions without retraining or additional simulation data.

Findings

Achieved low mean absolute errors in water level and velocity predictions.

Maintained accuracy across different time steps and initial conditions.

Enabled data-free surrogate modeling for nuclear thermal-hydraulic simulations.

Abstract

Severe accident analysis using system-level codes such as MELCOR is indispensable for nuclear safety assessment, yet the computational cost of repeated simulations poses a significant bottleneck for parametric studies and uncertainty quantification. Existing surrogate models accelerate these analyses but depend on large volumes of simulation data, while physics-informed neural networks (PINNs) enable data-free training but must be retrained for every change in problem parameters. This study addresses both limitations by developing the Parameterized PINNs coupled with FDM (P2F) method, a node-assigned hybrid framework for MELCOR's Control Volume Hydrodynamics/Flow Path (CVH/FP) module. In the P2F method, a parameterized Node-Assigned PINN (NA-PINN) accepts 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 conservation equation across all flow paths without retraining. This PINN is coupled with a finite difference method (FDM) solver that advances the mass conservation equation at each time step, ensuring exact discrete mass conservation while replacing the iterative nonlinear momentum solve with a single forward pass. Verification on a six-tank gravity-driven draining scenario yields a water level mean absolute error of $7.85 \times 10^{-5}$ m and a velocity mean absolute error of $3.21 \times 10^{-3}$ m/s under the nominal condition with $\Delta t = 1.0$ s. The framework maintains consistent accuracy across time steps ranging from 0.2 to 1.0 s and generalizes to five distinct initial conditions, all without retraining or simulation data. This work introduces a numerical coupling methodology for integrating parameterized PINNs with FDM within a nuclear thermal-hydraulic system code framework.