标题： 面向深度物理信息Kolmogorov-Arnold网络 显示英文标题

标题： Towards Deep Physics-Informed Kolmogorov-Arnold Networks

摘要： 自引入以来，Kolmogorov-Arnold Networks（KANs）已在多个领域成功应用，其中基于物理信息的机器学习（PIML）成为它们蓬勃发展的一个领域。 在PIML设置中，基于切比雪夫的物理信息KANs（cPIKANs）由于其计算效率而成为标准。 然而，与基于多层感知器的对应方法类似，当cPIKANs扩展到深度时，会面临重大挑战，导致训练不稳定，限制了它们在多个PDE问题中的应用。 为了解决这个问题，我们提出了一种与基无关的、类似Glorot的初始化方案，该方案保持激活值方差，并在稳定性与准确性方面显著优于cPIKANs的默认初始化。 受PirateNet架构的启发，我们进一步引入了残差门控自适应KANs（RGA KANs），旨在缓解深度cPIKANs中的发散问题，仅靠初始化已不足以解决这些问题。 通过实验测试和信息瓶颈分析，我们表明RGA KANs能够成功通过所有训练阶段，而基线cPIKANs在特定PDE设置中会在扩散阶段停滞。 在固定训练流程下，对七个标准前向PDE基准进行评估，结果显示RGA KANs在参数匹配的情况下始终优于cPIKANs和PirateNets——通常好几倍——同时在其他模型发散的设置中仍保持稳定。 显示英文摘要

摘要： Since their introduction, Kolmogorov-Arnold Networks (KANs) have been successfully applied across several domains, with physics-informed machine learning (PIML) emerging as one of the areas where they have thrived. In the PIML setting, Chebyshev-based physics-informed KANs (cPIKANs) have become the standard due to their computational efficiency. However, like their multilayer perceptron-based counterparts, cPIKANs face significant challenges when scaled to depth, leading to training instabilities that limit their applicability to several PDE problems. To address this, we propose a basis-agnostic, Glorot-like initialization scheme that preserves activation variance and yields substantial improvements in stability and accuracy over the default initialization of cPIKANs. Inspired by the PirateNet architecture, we further introduce Residual-Gated Adaptive KANs (RGA KANs), designed to mitigate divergence in deep cPIKANs where initialization alone is not sufficient. Through empirical tests and information bottleneck analysis, we show that RGA KANs successfully traverse all training phases, unlike baseline cPIKANs, which stagnate in the diffusion phase in specific PDE settings. Evaluations on seven standard forward PDE benchmarks under a fixed training pipeline with adaptive components demonstrate that RGA KANs consistently outperform parameter-matched cPIKANs and PirateNets - often by several orders of magnitude - while remaining stable in settings where the others diverge.