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.
arXiv:2512. 09084v3 Announce Type: replace Abstract: The Kolmogorov-Arnold representation theorem offers a theoretical alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate functions on edges rather than nodes.
By Oscar Eliasson
arXiv:2609.06660v1 Announce Type: cross
Abstract: Accurate aerodynamic prediction is critical for designing fuel-efficient and safe transportation systems such as aircraft and automobiles, yet tradit...
By Wenxuan Jin, Jianguo Yao, Haibing Guan, Xijun Li
arXiv:2609.38213v1 Announce Type: cross
Abstract: We introduce a dataset of approximately 10,000 Reynolds-Averaged Navier-Stokes (RANS) simulations of steady, incompressible, two-dimensional subsonic...
By Haitz S\'aez de Oc\'ariz Borde, Flavio Savarino, Andrei Cristian Popescu, Pietro Innocenzi, Pantelis Papageorgiou, Xerxes Xian Chong
arXiv:2606. 07724v1 Announce Type: new Abstract: High-fidelity computational fluid dynamics (CFD) is crucial to vehicle aerodynamic analysis, but its cost still constrains early-stage design exploration.
By Kangkang Qi, Huiyu Yang, Keqi Ding, Yunpeng Wang, Yuntian Chen, Yuanwei Bin, Rikui Zhang, Jianchun Wang
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
arXiv:2512. 07847v2 Announce Type: replace Abstract: Benchmarking has been the cornerstone of progress in computer vision, natural language processing, and the broader deep learning domain, driving algorithmic innovation through standardized datasets and reproducible evaluation protocols.
By Mohamed Elrefaie, Dule Shu, Matt Klenk, Faez Ahmed
arXiv:2609.17160v1 Announce Type: new
Abstract: Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysi...
By Lionel Salesses, Caroline Sainvitu, Tariq Benamara
arXiv:2607. 18309v1 Announce Type: new Abstract: Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight.
By Henrik Lange, Reik Thormann, Philipp Bekemeyer
Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs. Existing approaches are MLP- or flow-based and lack per-edge functional transparency; the only Kolmogorov--Arnold Network (KAN) variant with monotonicity, MonoKAN, enforces the constraint only on a restricted parameter subset and requires a projection-style training procedure.
arXiv:2606. 17886v1 Announce Type: new Abstract: Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs.
By Mikhail Krasnov, Carolina Fortuna, Bla\v{z} Bertalani\v{c}
arXiv:2607. 11672v1 Announce Type: new Abstract: Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs.
By Li Xiao, Tianyu Li, Yiye Zou, Mingjie Zhang, Xiaogangd Deng