Kolmogorov–Arnold networks for turbulence anisotropy mapping

This study evaluates the generalization performance and representation efficiency (parsimony) of a previously introduced Tensor Basis Kolmogorov–Arnold Network (TBKAN) architecture for data-driven turbulence modeling. The TBKAN framework replaces the multilayer perceptron (MLP) used in either the standard or modified Tensor Basis Neural Network (TBNN) with a Kolmogorov–Arnold network (KAN), which reduces the model complexity while providing a structure that can be used with symbolic regression to provide potentially a physical interpretability that is not available in a “black box” MLP. While some prior work demonstrated TBKAN's feasibility for modeling a “simple” flat plate boundary layer flow, this study extends the TBKAN architecture to model more complex benchmark flows, in particular, square duct and periodic hills flows, which exhibit strong turbulence anisotropy, secondary motion, and flow separation and reattachment. A realizability-informed loss function is employed to constrain the model predictions, and, for the first time, TBKAN predictions are stably injected into the Reynolds-averaged Navier–Stokes equations to provide a posteriori predictions of the mean velocity field. Results show that a TBKAN achieves comparable or slightly improved accuracy relative to a TBNN (based on an MLP), while using fewer parameters to achieve this performance in comparison to a TBNN, both TBNN and TBKAN successfully capture key flow features in the square duct and periodic hills flows (e.g., secondary motions of the second kind, separation and reattachment zones, etc.) and demonstrate a significantly improved predictive performance relative to the conventional k–ω shear-stress transport turbulence closure model.