Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs

2026-06-25

AI Summary

This study addresses the challenge of efficiently and accurately predicting surface pressure distributions on subsonic and transonic airfoils by introducing Kolmogorov–Arnold Networks (KANs)—based on the Kolmogorov–Arnold representation theorem—into aerodynamic surrogate modeling for the first time. The authors systematically compare KANs against Multilayer Perceptrons (MLPs) and Graph Neural Networks (GNNs). Experimental results demonstrate that KANs achieve effective prediction of pressure coefficient distributions with lower model complexity and faster training speeds, albeit with slightly lower accuracy than hyperparameter-optimized MLPs. While GNNs attain the highest predictive accuracy, they incur substantially greater computational costs. The work also highlights challenges associated with KANs, particularly regarding training stability and sensitivity to hyperparameters, thereby offering a novel architectural alternative and empirical benchmark for surrogate modeling in fluid dynamics.

Abstract

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

Problem

• Kolmogorov Arnold networks
• aerodynamic prediction
• surrogate modelling
• pressure distribution
• fluid dynamics

Innovation

• Kolmogorov-Arnold Networks
• aerodynamic surrogate modeling
• activation function learning
• fluid dynamics
• neural network comparison