Regional accuracy of physics-informed neural networks (PINNs) for recirculation in a deep lid-driven cavity

Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine datafree physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hardconstrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/hp calculations with the same Gaussian-regularized lid provide the reference fields. For D/W = 5 and Re = 100, 250, 500 and 1000, evaluation on a common 121×605 grid gives interior velocity RMS discrepancies of 6.542×10−3U to 9.541×10−3U and gauge-aligned pressure RMS discrepancies of 2.082× 10−3ρU2 to 5.838×10−3ρU2. Floor velocity RMS discrepancies range from 1.255×10−10U to 2.332×10−9U, where U is the lid-velocity scale. In a separate 161×801 assessment at Re = 1000, the refined workflow lowers interior velocity RMS discrepancy from 7.181×10−3U to 3.394× 10−3U and gauge-aligned pressure RMS discrepancy from 2.793×10−3ρU2 to 1.167×10−3ρU2. The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where localized rotational-field discrepancies remain substantial.