# Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor

arXiv: https://arxiv.org/abs/2605.30277 · HTML: https://mlsanity.com/paper/2605.30277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 5 of 5)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains](https://mlsanity.com/paper/2007.11207/) (2020)
- [Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions](https://mlsanity.com/paper/2504.10932/) (2025)
- [Node Assigned physics-informed neural networks for thermal-hydraulic system simulation: CVH/FL module](https://mlsanity.com/paper/2504.16447/) (2025)
- [Improving Variational Autoencoder using Random Fourier Transformation: An Aviation Safety Anomaly Detection Case-Study](https://mlsanity.com/paper/2601.01016/) (2026)

## Abstract (arXiv)

Real-time thermal-hydraulic simulation is essential for digital twin (DT) technology that supports the safe and efficient operation of small modular reactors (SMRs). Computational fluid dynamics (CFD) provides high-fidelity flow analysis, but its computational cost prevents direct use in DT applications. AI-based surrogate modeling has been actively investigated to address this limitation, yet neural operator--based surrogates for CFD-level transient analysis of SMR-specific geometries have not been reported. This study presents an integrated framework that combines a reduced-order model (ROM) with neural operators, applied to the helical coil steam generator (HCSG) of the System-integrated Modular Advanced Reactor (SMART). Two ROM strategies tailored to each CFD data type were compared, an MLP-based autoencoder (AE) for unstructured mesh data and a convolutional autoencoder (CAE) for structured mesh data, and each was coupled with the deep operator network (DeepONet) to construct the latent DeepONet (L-DeepONet). The Fourier neural operator (FNO) was additionally adopted for comparison. A multi-scale technique was incorporated into both frameworks to mitigate spectral bias and improve the prediction of K'arm'an vortex streets developing inside the HCSG. The multi-scale L-DeepONet captured the instantaneous periodic vortex dynamics in both velocity and pressure fields, while the FNO and its multi-scale variant predicted the time-averaged mean flow and provided reliable pressure drop estimates. These complementary characteristics provide a practical model-selection guideline that links each architecture to specific DT objectives based on CFD data type and the required level of flow resolution.