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

arXiv: https://arxiv.org/abs/2604.02663 · HTML: https://mlsanity.com/paper/2604.02663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Parallel Physics-Informed Neural Networks via Domain Decomposition](https://mlsanity.com/paper/2104.10013/) (2021)
- [Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations](https://mlsanity.com/paper/2005.05092/) (2020)
- [Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learning](https://mlsanity.com/paper/2206.06817/) (2022)
- [Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows](https://mlsanity.com/paper/2105.03332/) (2021)
- [Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modeling](https://mlsanity.com/paper/2504.11383/) (2025)
- [Comparison of CNN-based deep learning architectures for unsteady CFD acceleration on small datasets](https://mlsanity.com/paper/2502.06837/) (2025)
- [Node Assigned physics-informed neural networks for thermal-hydraulic system simulation: CVH/FL module](https://mlsanity.com/paper/2504.16447/) (2025)

## Abstract (arXiv)

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 × 10-5 m and a velocity mean absolute error of 3.21 × 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.