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Abstract - Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs
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.
Kolmogorov-Arnold网络在气动预测中的应用:与MLP和GNN的比较 /
Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs
1️⃣ 一句话总结
该研究将一种新型神经网络架构——KAN(基于Kolmogorov-Arnold定理,通过训练激活函数而非传统权重)应用于飞机机翼表面压力分布的空气动力学预测,发现虽然KAN模型复杂度低、训练快,但性能略逊于精心调参的传统MLP,且训练不稳定,效果高度依赖超参数优化,而图神经网络(GNN)表现最佳但训练耗时最长。