A parametric physics-informed neural network framework for cylinder-induced thermal flows

Thermal design and monitoring of compact heat exchangers require fields across changing operating conditions, and increasingly from a few embedded sensors, yet each new Reynolds number is a new mesh-based simulation. A physics-informed neural network (PINN) framework is presented for the coupled prediction and inverse recovery of velocity, pressure, temperature, and vorticity fields in laminar forced convection past a heated circular cylinder at Pr=0.71 and Re∈[20,200]. A single Reynolds-number-augmented parametric PINN, implemented in PyTorch and trained once over the full range, predicts unseen Reynolds numbers with relative L2 velocity error εU=0.68% and average Nusselt number deviation below 0.7% from an OpenFOAM finite volume reference, against 3.82% for a Deep Operator Network and 6.54% for a graph neural network, without retraining. Hard boundary condition enforcement through a smooth distance function output transformation, an auxiliary vorticity transport residual, residual adaptive collocation resampling, and gradient normalization loss weighting act synergistically to yield a divergence error of 2.1×10−4 and an 86% cumulative reduction in velocity error over the unaugmented baseline. Promoting the Reynolds number to a co-optimized scalar parameter recovers an unknown Re from ten sparse pressure observations with mean relative error 0.45%. Integral quantities agree with experiment: Nu¯ rises from 3.06 to 9.54 across the range, within 1.6% of classical correlations, and St=0.166 and 0.194 match measurements to within 1%. Conservation metrics on held-out grids confirm constraint satisfaction, and inference is approximately 3000× faster than the finite volume solver, giving a physically consistent surrogate for real-time monitoring of sensor sparse thermal infrastructure.