Kolmogorov-Arnold Networks for Data-Driven Turbulence Modeling

Kolmogorov-Arnold Networks (KAN) is a newly proposed deep learning technique. This novel architecture utilizes the Kolmogorov-Arnold representation theorem, which distinguishes this model with the conventional multi-layer perceptron (MLP) approach. Instead of training the weights and biases with fixed activation functions like the standard neural networks, KAN enables us to learn the activation functions that replace the weights in conventional neural networks. As a result, KAN has no trainable weights in its architecture. The KAN architecture relies on the superposition of several activation functions to model any arbitrary function. Additionally, this architecture can also provide a better interpretability aspect of our model. To examine the capability of this new architecture, this paper aims to implement this architecture for turbulence modelling. Therefore, in this paper, we developed a data-driven turbulence model using KAN. This model takes input features from the mean flow properties and predicts the Reynolds stresses as the main quantity of interest. Our findings indicate that KAN can rival the capabilities of a standard neural network model while employing simpler architecture, despite its more expensive training cost. In this work, we also tested the capability of KAN to perform symbolic regression.