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

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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.

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arXiv Machine Learning
Jun 26

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

arXiv:2606. 27126v1 Announce Type: new 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).

By Miguel Jaraiz, Fermin Gutierrez, Pablo Yeste, Miguel S\'anchez-Dom\'inguez, Eusebio Valero, Gonzalo Rubio, Lucas Lacasa
arXiv Machine Learning
2d ago

Airfoil2Vec: Spectral Geometry-Conditioned Neural Surrogate Models for Airfoil Aerodynamics and a Downforce-Generating CFD Dataset

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By Haitz S\'aez de Oc\'ariz Borde, Flavio Savarino, Andrei Cristian Popescu, Pietro Innocenzi, Pantelis Papageorgiou, Xerxes Xian Chong
arXiv Machine Learning
1d ago

Neural scaling laws and evolution of learnable activation functions of Kolmogorov-Arnold networks

The paper studies Kolmogorov‑Arnold Networks (KANs), a neural architecture that treats activation functions as learnable components, offering improved interpretability for scientific applications. It investigates how KANs scale with dataset size on image classification tasks (MNIST, Fashion‑MNIST) and a magnetic‑parameter regression task, revealing a broken neural scaling law that transitions from a faster to a slower decay of test loss as data grows. The authors also analyze how the learned activation functions evolve from simple linear approximations to more complex, interpretable symbolic forms as more data is provided.

By Tilen Cadez, Sanghoon Lee, Kyoung-Min Kim