Graph neural networks (GNNs) excel in learning from network-like data but
often lack interpretability, making their application challenging in domains
requiring transparent decision-making. We propose the Graph Kolmogorov-Arnold
Network (GKAN), a novel GNN model leveraging spline-based activation functions
on edges to enhance both accuracy and interpretability. Our experiments on five
benchmark datasets demonstrate that GKAN outperforms state-of-the-art GNN
models in node classification, link prediction, and graph classification tasks.
In addition to the improved accuracy, GKAN's design inherently provides clear
insights into the model's decision-making process, eliminating the need for
post-hoc explainability techniques. This paper discusses the methodology,
performance, and interpretability of GKAN, highlighting its potential for
applications in domains where interpretability is crucial.

Graph neural network 模型 GKAN 通过使用基于样条函数的边缘激活函数，提高了准确性和解释性，在节点分类、链接预测和图分类任务上胜过了最先进的图神经网络模型。此外，GKAN 的设计本身提供了对模型决策过程的清晰见解，消除了事后解释性技术的需求。

科尔莫戈洛夫 - 阿诺德图神经网络

Kolmogorov-Arnold Graph Neural Networks

We present a novel approach to predicting the pressure and flow rate of
flexible electrohydrodynamic pumps using the Kolmogorov-Arnold Network.
Inspired by the Kolmogorov-Arnold representation theorem, KAN replaces fixed
activation functions with learnable spline-based activation functions, enabling
it to approximate complex nonlinear functions more effectively than traditional
models like Multi-Layer Perceptron and Random Forest. We evaluated KAN on a
dataset of flexible EHD pump parameters and compared its performance against
RF, and MLP models. KAN achieved superior predictive accuracy, with Mean
Squared Errors of 12.186 and 0.001 for pressure and flow rate predictions,
respectively. The symbolic formulas extracted from KAN provided insights into
the nonlinear relationships between input parameters and pump performance.
These findings demonstrate that KAN offers exceptional accuracy and
interpretability, making it a promising alternative for predictive modeling in
electrohydrodynamic pumping.

我们提出了一种新颖的方法，使用 Kolmogorov-Arnold 网络预测柔性电流体力泵的压力和流量。通过受到 Kolmogorov-Arnold 表示定理的启示，KAN 通过可学习的基于样条的激活函数代替固定的激活函数，使其比传统模型如多层感知器和随机森林更有效地逼近复杂的非线性函数。我们在柔性 EHD 泵参数的数据集上评估了 KAN，并将其性能与 RF 和 MLP 模型进行了比较。KAN 取得了较高的预测准确性，在压力和流量预测方面的均方误差分别为 12.186 和 0.001。从 KAN 中提取的符号公式揭示了输入参数与泵性能之间的非线性关系。这些发现表明，KAN 具有出色的准确性和可解释性，使其成为电流体力泵预测建模中有希望的替代方法。