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

2026-06-25 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Engineering & Applied Sciences, Mathematics & Computational Sciences · Depth: Advanced, medium

Summary

Kolmogorov Arnold networks (KANs), a neural network architecture with trainable activation functions, were assessed for aerodynamic prediction, specifically forecasting surface pressure distribution on subsonic and transonic airfoils. This study compared KANs against traditional deep multilayer perceptrons (MLPs) and graph neural networks (GNNs). KAN models demonstrated good performance in predicting pressure coefficients and interpolating across Mach numbers and angles of attack. However, their performance was found to be comparable, and marginally inferior, to a suitably trained MLP. GNNs achieved the best performance in this task, though at the cost of longer training times. While KANs typically exhibit lower complexity and faster training, they are prone to training instabilities and require extensive hyperparameter optimization for optimal results.

Key takeaway

For Machine Learning Engineers developing aerodynamic surrogate models, if you are evaluating neural network architectures, recognize that while Kolmogorov Arnold networks (KANs) offer lower complexity and faster training, their performance is marginally inferior to well-tuned MLPs and they demand rigorous hyperparameter optimization to mitigate training instabilities. You should prioritize GNNs for peak accuracy, but consider KANs for scenarios where computational efficiency during training is paramount, provided you invest heavily in hyperparameter search.

Key insights

KANs show promise in fluid dynamics but face stability issues and are marginally inferior to MLPs for aerodynamic prediction.

Principles

• KANs adapt activation functions, not affine coefficients.
• KANs offer universal approximation properties.
• Lower complexity KANs can train faster than MLPs/GNNs.

Method

The study assessed KAN, MLP, and GNN performance by predicting surface pressure distribution over subsonic and transonic airfoils, interpolating across Mach numbers and angles of attack.

In practice

• KANs can interpolate across fluid dynamics parameters.
• Consider KANs for lower complexity surrogate models.
• Prioritize hyperparameter tuning for KAN stability.

Topics

• Kolmogorov Arnold Networks
• Aerodynamic Prediction
• Multilayer Perceptrons
• Graph Neural Networks
• Fluid Dynamics
• Surrogate Modeling

Code references

• hoangthangta/All-KAN
• hoangthangta/BSRBF_KAN

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.