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

arXiv: https://arxiv.org/abs/2606.27126 · HTML: https://mlsanity.com/paper/2606.27126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Torch.manual_seed(3407) is all you need: On the influence of random seeds in deep learning architectures for computer vision](https://mlsanity.com/paper/2109.08203/) (2021)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries](https://mlsanity.com/paper/2408.02950/) (2024)
- [Kolmogorov-Arnold Network for Online Reinforcement Learning](https://mlsanity.com/paper/2408.04841/) (2024)
- [Addressing common misinterpretations of KART and UAT in neural network literature](https://mlsanity.com/paper/2408.16389/) (2024)
- [Towards certification: A complete statistical validation pipeline for supervised learning in industry](https://mlsanity.com/paper/2411.02075/) (2024)
- [Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints](https://mlsanity.com/paper/2505.02634/) (2025)
- [A Certifiable Machine Learning-Based Pipeline to Predict Fatigue Life of Aircraft Structures](https://mlsanity.com/paper/2509.10227/) (2025)
- [FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes](https://mlsanity.com/paper/2604.08586/) (2026)

## Abstract (arXiv)

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.