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

2026-04-02

AI Summary

This work addresses the high computational cost of repeated simulations in traditional nuclear thermal-hydraulic system codes like MELCOR for parametric studies and uncertainty quantification, as well as the data dependency of conventional surrogate models and the need for retraining in physics-informed neural networks (PINNs) under varying parameters. To overcome these limitations, the authors propose the P2F method, which uniquely couples a parameterized node-allocated PINN (NA-PINN) with the finite difference method (FDM) to form a hybrid solver that requires neither training data nor retraining. This framework replaces the nonlinear iterative solution of momentum equations in MELCOR by decoupling momentum and mass conservation equations. Validated on a six-tank gravity-driven draining scenario across diverse initial conditions and time steps (Δt = 0.2–1.0 s), the method achieves high accuracy with mean absolute errors of 7.85×10⁻⁵ m in water level and 3.21×10⁻³ m/s in velocity, effectively balancing computational efficiency and conservation fidelity.

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 $Δt = 1.0$ 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.

Problem

• severe accident analysis
• surrogate modeling
• physics-informed neural networks
• parameterized simulation
• thermal-hydraulic systems

Innovation

• Parameterized PINNs
• Finite Difference Method
• Thermal-Hydraulic Simulation
• Surrogate Modeling
• Momentum Conservation