Embedding flow-field similarity priors for sparse-data turbulence reconstruction

Reconstructing three-dimensional turbulent thermal-hydraulic fields from sparse observations is important for online monitoring and digital-twin applications. However, complex spatial structures, difficult optimization, and long training times continue to limit the application of physics-informed neural networks (PINNs) to three-dimensional turbulent-flow reconstruction. This study proposes a Similarity-Enhanced Physics-Informed Neural Network (SE-PINN) for thermal-hydraulic field reconstruction in nuclear reactor rod-bundle channels. The proposed method introduces a representative reference field as a geometry-conditioned physical prior and combines its local features with continuous three-dimensional coordinates and operating-condition parameters. Based on these inputs, the network directly predicts the thermal-hydraulic fields under the target operating condition, including velocity, pressure, and temperature. Sparse labeled CFD observations are incorporated through the data loss, while three-dimensional effective-property Reynolds-averaged Navier–Stokes residuals constrain mass, momentum, and energy conservation. The model is evaluated under previously unseen interpolation and extrapolation conditions. With 80 labeled observation points per axial cross-section, the aggregate relative L 2 error over U, V, P, and T is 1.90%, with an aggregate R 2 of 0.9996. The operating-condition-level relative L 2 errors are 1.06% and 2.17% for the interpolation and extrapolation groups, respectively. Detailed comparisons under the maximum-flow extrapolation condition show that the model reproduces the principal transverse-flow structures, vortex topology, and their downstream evolution. The reference-field-enhanced model reduces the weighted total training loss to 3.66 × 10 − 5 within 100 epochs, whereas the baseline PINN without the reference-field input remains at approximately 5.49 × 10 − 3 after extended training. After offline training, the end-to-end reconstruction time for a complete operating condition is approximately 0.32 s. These results demonstrate that the SE-PINN provides accurate and efficient reconstruction of three-dimensional thermal-hydraulic fields under sparse supervision, supporting rapid state estimation across a range of operating conditions.