To improve unified modeling of steady two-dimensional lid-driven cavity flow across a wide range of Reynolds numbers, this study proposes a Vorticity-Enhanced Physics-Informed Neural Network (VE-PINN). The method augments a standard velocity-pressure PINN with a vorticity-transport residual and uses a logarithmic Reynolds-number embedding, log10Re, for multi-regime training. Using CFD benchmark data as supervision and evaluation, we conduct systematic ablation studies on network architecture, loss weighting, sampling density, input embedding, and physical constraint over Re=1000−50000, together with out-of-range extrapolation tests. The results show that the logarithmic Reynolds-number embedding improves cross-regime training stability and reduces the multi-regime mean relative error, while the vorticity-transport constraint improves the reconstruction of velocity fields and secondary vortical structures with only a modest increase in training cost. Further comparisons based on contour fields, centerline velocity profiles, vortex-core locations, and vorticity intensity indicate that VE-PINN provides improved accuracy, physical consistency, and generalization relative to the baseline PINN in the present benchmark. These findings suggest that, for the steady cavity-flow problem considered here, combining logarithmic parameter embedding with derivative-level physical constraint is a practical and effective strategy for parametric PINN modeling.
Zheng et al. (Thu,) studied this question.