# Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor Source: [Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor]() Collection index: [llms.txt]() Data updated: 2026-05-30T05:00:11.986Z Authors: Minseo Lee, Seongmin Oh, Chaehyeon Song, Bumjin Cho, Shilaj Baral, Sangam Khanal, Minseop Song, Joongoo Jeon Published: 2026-05-28T17:33:22.000Z ## Abstract 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\\'{a}rm\\'{a}n 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Flow field prediction on HCSG tube bundle 0.4 m/s inlet velocity (test)](): Flow Field Prediction; HCSG tube bundle 0.4 m/s inlet velocity (test); Point-wise Metric P1: 4.765. - [Fluid Flow Prediction on HCSG tube bundle inlet velocity 0.7 m/s](): Fluid Flow Prediction; HCSG tube bundle inlet velocity 0.7 m/s; Error P1: 5.71. - [Pressure drop prediction on Pressure Drop Prediction Dataset Inlet 0.7 m/s](): Pressure drop prediction; Pressure Drop Prediction Dataset Inlet 0.7 m/s; Mean Relative Error: 1.92. - [Pressure drop prediction on Pressure Drop Prediction Dataset (Inlet 0.4 m/s)](): Pressure drop prediction; Pressure Drop Prediction Dataset (Inlet 0.4 m/s); Mean Relative Error: 1.24. - [Pressure field prediction on HCSG Inlet 0.7 m/s (test)](): Pressure field prediction; HCSG Inlet 0.7 m/s (test); Mean Relative L2 Error: 18.19. - [Pressure field prediction on HCSG Inlet 0.4 m/s (test)](): Pressure field prediction; HCSG Inlet 0.4 m/s (test); Mean Relative L2 Error: 14.5. - [Velocity field prediction on HCSG Inlet 0.4 m/s (test)](): Velocity field prediction; HCSG Inlet 0.4 m/s (test); Mean Relative L2 Error: 8.31. - [Velocity field prediction on HCSG Inlet 0.7 m/s (test)](): Velocity field prediction; HCSG Inlet 0.7 m/s (test); Mean Relative L2 Error: 0.1172. ## Original sources and implementation [Original paper]() [PDF]()