High-fidelity Modeling of Full-scale Pressurized Water Reactor Flow Fields for Machine Learning Applications
Authors: Logan A. Burnett, Hyungjun Kim, Hsien-Cheng Chou, Arsha Witoelar, Robert A. Brewster, Benoit Forget, Emilio Baglietto, Majdi I. Radaideh
Organizations: Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, United States · Korea Atomic Energy Research Institute, Daejeon, 34057, South Korea · Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, United States · Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, United States · Department of Computer Science and Engineering, University of Michigan, Ann Arbor, MI 48109, United States
This work presents a high-fidelity computational fluid dynamics (CFD) and data-driven modeling framework for assembly-level flow characterization in a four-loop pressurized water reactor (PWR). A full lower-plenum and core-inlet domain was constructed using publicly available geometry and operating conditions, enabling transient simulations with pump-induced swirl boundary conditions. The results show that cold-leg swirl and lower-plenum transport generate strongly heterogeneous assembly-wise inlet flow distributions, particularly near the lower core region, while axial resistance and mixing progressively homogenize the flow at higher elevations. These physics-informed datasets were subsequently used to evaluate machine learning (ML) applications for partial field reconstruction and short-term autoregressive prediction. A 3D convolutional-based inpainting model successfully recon-structed missing assembly-level mass flow rates from partial observations, with errors concentrated in the highly turbulent base (bottom) layer and diminishing significantly in upper layers. Comparative analysis across multiple ML models demon-strates that spatially aware architectures, particularly ConvLSTM, significantly outperform sequence-based (LSTM) and operator-learning (DeepONet) approaches by effectively capturing coupled spatio-temporal dynamics. The study also high-lights key challenges, including the sensitivity of inlet flow predictions to turbulence and mesh resolution, as well as the absence of full-scale experimental validation data. Despite these limitations, the results remain consistent with expected physical behavior. Overall, this work establishes high-fidelity CFD as a critical foundation for developing data-driven surrogates, sparse sensing strategies, and future multiphysics coupling frameworks.
The simulation of fluid flows is computationally expensive due to the complexity of its governing partial differential equations. Machine learning models offer a potential surrogate, enabling learning from simulations and significantly faster predictions of flow fields. However, these models require large training datasets, which introduces a trade-off between dataset generation cost and predictive accuracy. In this work, we investigate the relationship between the size of the training-set and accuracy of the prediction when learning steady flow fields in an industrial-scale stirred vessel. A data set of steady flows is generated using Reynolds Averaged Navier Stokes (RANS) simulations in a range of realistic operating conditions, including impeller speeds and liquid heights. We train implicit neural representations of flow fields and compare purely data-driven and constrained variants. Model performance is evaluated using global mean squared error (MSE), qualitative spatial comparisons of predicted and reference flow fields, and tracer transport simulations. We find that the prediction error decreases monotonically with increasing training data, but also that it exhibits clear diminishing returns beyond moderate dataset sizes. Physics-based constraints significantly improve accuracy and reduce variability across training runs in low-data regimes, and they lead to more stable tracer-transport behavior. Furthermore, reasonable interpolation can be achieved over different impeller speeds and liquid heights. However, these benefits come with an increase in the complexity of training, and their relative advantage diminishes as the training set grows.
Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of 2.70×10−4, compared with 4.02×10−4 for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.
Deep learning surrogates for CFD flow-field prediction often rely on large, complex models, which can be slow and fragile when data are noisy or incomplete. We introduce FlowForge, a staged local rollout engine that predicts future flow fields by compiling a locality-preserving update schedule and executing it with a shared lightweight local predictor. Rather than producing the next frame in a single global pass, FlowForge rewrites spatial sites stage by stage so that each update conditions only on bounded local context exposed by earlier stages. This compile-execute design aligns inference with short-range physical dependence, keeps latency predictable, and limits error amplification from global mixing. Across PDEBench, CFDBench, and BubbleML, FlowForge matches or improves upon strong baselines in pointwise accuracy, delivers consistently better robustness to noise and missing observations, and maintains stable multi-step rollout behavior while reducing per-step latency.