Turbulent channel flow: A physics-informed neural network approach with embedded parameter optimization

Wall-bounded turbulence modeling is fundamentally limited by the representation of the logarithmic law, yet its parameters such as the von Kármán constant, κ, and intercept, B, and its spatial bounds (ylow+, yhigh+) are often assumed a priori. Here we present a hybrid optimization – physics-informed neural network (PINN) framework that directly addresses this point. The method's novelty is a two-stage process: first, an optimization pre-processing step uses direct numerical dimulation data to calibrate the log-law constants (κ,B) and (ylow+, yhigh+). Next, these values are hard-coded into a PINN, whose loss function constrains the solution to obey both the governing Reynolds-averaged Navier–Stokes equations and the log-law within its identified region. By accurately delineating the log-layer we prevent the PINN from enforcing incorrect physics in the viscous sublayer, which is essential for obtaining physically consistent velocity profiles and their derivatives. This method suggests a more universal and accurate model across various Reynolds numbers, thereby enabling the development of data-informed, physics-grounded turbulence closures.