# Node Assigned physics-informed neural networks for thermal-hydraulic system simulation: CVH/FL module

arXiv: https://arxiv.org/abs/2504.16447 · HTML: https://mlsanity.com/paper/2504.16447/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications](https://mlsanity.com/paper/2004.04276/) (2020)
- [L-HYDRA: Multi-Head Physics-Informed Neural Networks](https://mlsanity.com/paper/2301.02152/) (2023)
- [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)
- [Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective](https://mlsanity.com/paper/2401.08667/) (2024)
- [Comparison of CNN-based deep learning architectures for unsteady CFD acceleration on small datasets](https://mlsanity.com/paper/2502.06837/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation](https://mlsanity.com/paper/2604.02663/) (2026)
- [Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor](https://mlsanity.com/paper/2605.30277/) (2026)

## Abstract (arXiv)

Severe accidents (SAs) in nuclear power plants have been analyzed using thermal-hydraulic (TH) system codes such as MELCOR and MAAP. These codes efficiently simulate the progression of SAs, while they still have inherent limitations due to their inconsistent finite difference schemes. The use of empirical schemes incorporating both implicit and explicit formulations inherently induces unidirectional coupling in multi-physics analyses. The objective of this study is to develop a novel numerical method for TH system codes using physics-informed neural network (PINN). They have shown strength in solving multi-physics due to the innate feature of neural networks-automatic differentiation. We propose a node-assigned PINN (NA-PINN) that is suitable for the control volume approach-based system codes. NA-PINN addresses the issue of spatial governing equation variation by assigning an individual network to each nodalization of the system code, such that spatial information is excluded from both the input and output domains, and each subnetwork learns to approximate a purely temporal solution. In this phase, we evaluated the accuracy of the PINN methods for the hydrodynamic module. In the 6 water tank simulation, PINN and NA-PINN showed maximum absolute errors of 1.678 and 0.007, respectively. It should be noted that only NA-PINN demonstrated acceptable accuracy. To the best of the authors' knowledge, this is the first study to successfully implement a system code using PINN. Our future work involves extending NA-PINN to a multi-physics solver and developing it in a surrogate manner.