FEKAN：特征增强的柯尔莫哥洛夫-阿诺尔德网络
FEKAN: Feature-Enriched Kolmogorov-Arnold Networks
AI总结：
FEKAN通过特征增强提升KAN的计算效率和预测精度，适用于函数逼近、物理信息建模和神经算子设置。
摘要：
柯尔莫哥洛夫-阿诺尔德网络（KANs）最近作为一种有吸引力的替代多层感知机出现，通过函数分解提供增强的可解释性。然而，现有的KAN架构，包括样条、小波、径向基变体等，存在计算成本高和收敛慢的问题，限制了可扩展性和实用性。在此，我们引入了特征增强的柯尔莫哥洛夫-阿诺尔德网络（FEKAN），一种简单而有效的扩展，保留了KAN的所有优势，通过特征增强提高计算效率和预测准确性，而无需增加可训练参数的数量。通过纳入这些额外特征，FEKAN加速了收敛，增加了表示能力，并显著减轻了当前最先进KAN架构的计算开销特征。我们对FEKAN进行了全面的基准测试，包括函数逼近任务、适用于各种偏微分方程（PDEs）的物理信息公式，以及将输入和输出函数空间映射的神经算子设置。在函数逼近方面，我们系统地将FEKAN与广泛的KAN变体进行比较，包括FastKAN、WavKAN、ReLUKAN、HRKAN、切比雪夫KAN、RBFKAN以及原始SplineKAN。在所有任务中，FEKAN都表现出显著更快的收敛速度和比底层基线架构一致更高的逼近准确性。我们还建立了FEKAN的理论基础，证明其比KAN更优越的表示能力，这有助于提高准确性和效率。
英文摘要：
Kolmogorov-Arnold Networks (KANs) have recently emerged as a compelling alternative to multilayer perceptrons, offering enhanced interpretability via functional decomposition. However, existing KAN architectures, including spline-, wavelet-, radial-basis variants, etc., suffer from high computational cost and slow convergence, limiting scalability and practical applicability. Here, we introduce Feature-Enriched Kolmogorov-Arnold Networks (FEKAN), a simple yet effective extension that preserves all the advantages of KAN while improving computational efficiency and predictive accuracy through feature enrichment, without increasing the number of trainable parameters. By incorporating these additional features, FEKAN accelerates convergence, increases representation capacity, and substantially mitigates the computational overhead characteristic of state-of-the-art KAN architectures. We investigate FEKAN across a comprehensive set of benchmarks, including function-approximation tasks, physics-informed formulations for diverse partial differential equations (PDEs), and neural operator settings that map between input and output function spaces. For function approximation, we systematically compare FEKAN against a broad family of KAN variants, FastKAN, WavKAN, ReLUKAN, HRKAN, ChebyshevKAN, RBFKAN, and the original SplineKAN. Across all tasks, FEKAN demonstrates substantially faster convergence and consistently higher approximation accuracy than the underlying baseline architectures. We also establish the theoretical foundations for FEKAN, showing its superior representation capacity compared to KAN, which contributes to improved accuracy and efficiency.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
