A hard-constrained physics-informed neural network for localized digital twin modeling

Constructing high-fidelity, real-time 3D digital twins for critical local regions is essential for the safe operation of advanced nuclear energy systems. However, conventional CFD-based full-order models are computationally expensive and struggle to meet real-time simulation demands, while mainstream data-driven reduced-order models suffer from weak interpretability and poor extrapolation capabilities. Physics-Informed Neural Networks (PINNs) offer a promising approach for integrating physical principles with data, yet the prevalent soft-constraint paradigm faces limitations such as inadequate strict enforcement of physical laws, difficulties in balancing loss weights, and challenges in handling missing boundary information in local modeling. To address these issues, this study proposes a novel hard-constrained PINN method. The core of this approach lies in reconstructing the pressure Poisson equation into an explicit algebraic relationship between velocity and pressure mode coefficients via proper orthogonal decomposition and Galerkin projection, which is embedded into the neural network's forward propagation process, ensuring strict adherence to physical laws. Validation on an unsteady 3D finite square cylinder flow case demonstrates the superior performance of the proposed method over soft-constrained approaches: it reduces the extrapolation mean absolute error by 48.1%, with enhanced robustness; achieves faster, more stable convergence with 20.6% fewer training epochs and reduced sensitivity to physical weights; and saves 30.2% in prediction time while achieving comparable accuracy with a more lightweight network. This study provides a reliable and efficient technical pathway for constructing high-dimensional localized digital twins with limited boundary information.