Two-step high-resolution reconstruction of mean flow field and Reynolds stress distributions using physics-informed neural networks in a two-dimensional street canyon

• Physics-informed neural networks (PINNs) are employed to reconstruct canyon flow. • A two-step framework is proposed to capture mean velocity and fluctuation terms. • Standard deviations are introduced as outputs to alleviate training imbalance. • Pressure and Reynolds shear stress are accurately estimated without measurements. Physics-informed neural networks (PINNs) have shown great potential for flow reconstruction but continue to face challenges in training efficiency and prediction accuracy, particularly in complex turbulent problems in built environments. In this study, we propose a two-step reconstruction PINN model to accurately estimate the mean flow field, pressure, and turbulent statistics using sparse measurement data within a two-dimensional urban street canyon. The first-step PINN predicts mean velocity and surface pressure, which are resampled and used as training data for the second-step PINN to refine predictions of other physical quantities in the Reynolds-Averaged Navier–Stokes equations. Additionally, we investigate the effect of output variable scaling by comparing two approaches: directly using Reynolds stress terms and using standard deviations. Our findings indicate that although both the one-step (vanilla) and two-step reconstructions effectively capture key flow features, the two-step approach yields more accurate predictions across all output quantities. By enforcing velocity components as hard constraints, the second-step PINN can more effectively focus on other relevant variables in the governing equations. Furthermore, balancing output variable scaling improves predictions for all quantities, especially for Reynolds shear stress, which is 10–100 times smaller than other variables. This approach effectively mitigates the neglect of residuals associated with small-scale values compared to conventional methods. The proposed method demonstrates strong performance in reconstructing mean flow fields with complex turbulent fluctuations, highlighting its potential for developing robust and practical PINNs for urban wind analysis and industrial applications.