DNS-Calibrated Physics-Informed Neural Networks with Learnable Constants for Reynolds Number Extrapolation in Turbulent Channel Flows

This paper employs Physics-Informed Neural Networks (PINNs) for the reconstruction and modelling of mean velocity profiles in fully developed turbulent channel flow over a high friction Reynolds number (Reτ). The network is trained with a high-fidelity Direct Numerical Simulation (DNS) dataset from channel flows, for Reτ=395–4186, and can extrapolate up to Reτ = 10,049. The model predicts the mean velocity in terms of the inner-law variables, u+, across Reynolds numbers using the inputs η=y+/Reτ and Reτ. A key novelty is the simultaneous optimisation of the network weights alongside two fundamental turbulence parameters, i.e., the von Kármán constant (κ) and the van Driest damping constant (A+), allowing the PINN to autonomously calibrate the near-wall damping and log-law scaling directly from the physics-augmented loss function. The model performance is evaluated using profile-based metrics (R2, mean square and absolute error) and integrated quantities (V¯+, Reb, and the skin-friction coefficient Cf), with comparisons against DNS-integrated friction values and classical theoretical values. The resulting hybrid framework offers a promising foundation for real-time digital twins and the acceleration of Computational Fluid Dynamics (CFD) solvers in canonical wall-bounded flows. By establishing a physically grounded connection between sparse data and structural constraints, these models enable accurate extrapolation into high Reynolds number regimes where the computational costs of traditional high-fidelity simulations are otherwise prohibitive.