Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training

Data-driven turbulence closures are usually calibrated by inverse methods that place a CFD solver inside the optimization loop, tying the learned model to a particular discretization and requiring every intermediate iterate to converge. We instead train closures inside a physics-informed neural network (PINN): the RANS residual is imposed by automatic differentiation, making the inverse problem mesh-free, differentiable, and solver-agnostic. Because no forward solve runs during training, only the final closure must be solver-stable, arbitrary neural closures are admitted without deriving adjoints, and iterative solver costs are avoided. Each constitutive hypothesis trains in minutes on a single GPU, enabling rapid screening of closure forms. We develop four closures: three model the Reynolds stress on a tensor basis with built-in realizability (a local map, a non-local model transporting turbulent kinetic energy, and the same with a learned length scale l), while a fourth models the Reynolds force F = -\nabla \cdot \tau directly, free of realizability constraints. The closures are trained across six 2D bluff-body wakes at Re = 10^4 and deployed frozen in a finite-element solver. Coupled stability is enhanced by input-gradient smoothing and a Lipschitz constraint. We assess closures in-sample and under a strict leave-one-shape-out (LOSO) protocol. All four improve substantially on a steady SST k-\omega baseline. The learned-length-scale stress closure is most accurate on stress fields, while transporting kinetic energy is decisive for generalization. Notably, the force model generalizes best and attains the lowest out-of-sample error on mean velocity and drag (LOSO drag error ~8.5%). Finally, we show these closures can be efficiently trained on PIV data, enabling data-driven modeling for geometries intractable for DNS.