Kolmogorov-Arnold Networks for Turbulence Anisotropy Mapping

TL;DR

This paper extends the Tensor Basis Kolmogorov-Arnold Network (TBKAN) for complex turbulence flows, demonstrating its efficiency, physical interpretability, and stable integration into RANS simulations for anisotropic turbulence modeling.

Contribution

The study introduces an extended TBKAN architecture for complex turbulence flows, enhancing model interpretability and stability in RANS simulations.

Findings

TBKAN reduces model complexity compared to MLP-based models.

Stable integration of TBKAN into RANS yields accurate mean velocity predictions.

Extension to complex flows like square duct and periodic hills demonstrated effectiveness.

Abstract

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 multi-layer perceptron (MLP) used in either the standard or modified Tensor Basis Neural Network (TBNN) with a Kolmogorov-Arnold network (KAN), which significantly reduces the model complexity while providing a structure that potentially can be used with symbolic regression to provide 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 it a posteriori predictions of the mean velocity field.