Turbulence Closure Modeling Using Kolmogorov-Arnold Networks and Bayesian Optimization

Abstract

This thesis presents two complementary approaches to improving Reynolds-averaged Navier–Stokes (RANS) turbulence modeling through machine learning and optimization. First, we introduce a realizability-informed framework for training stable and physically consistent machine learning-based anisotropy closures within the tensor basis neural network (TBNN) paradigm. We develop a physics-based loss function that penalizes non-realizable predictions during training, enhancing model stability and generalization. To reduce model complexity and improve interpretability, we replace conventional multilayer perceptrons (MLPs) with Kolmogorov–Arnold Networks (KANs), forming the Tensor Basis KAN (TBKAN) architecture. The TBKAN framework is evaluated across three canonical flows, flat plate, periodic hills, and square duct, demonstrating improved prediction fidelity, stability, and realizability compared to baseline TBNNs and traditional eddy-viscosity models.

Second, we explore the application of Bayesian optimization for data-driven calibration of RANS model coefficients, focusing on the generalized k–omega (GEKO) model. The proposed turbo-RANS framework is applied to a converging-diverging channel flow case characterized by adverse pressure gradients and separation. Optimized coefficients yield improved predictions of wall-bounded quantities and streamwise velocity profiles when compared against direct numerical simulation (DNS) and large eddy simulation (LES) references.

Together, these contributions address key limitations in existing data-driven turbulence modeling approaches, namely, lack of physical realizability, interpretability, and predictive robustness, while providing practical tools for improved RANS performance in engineering flows. All code and models developed in this work are made publicly available to encourage further research and adoption.