KAN 能否成为 CAN？输入凸 Kolmogorov-Arnold 网络（KAN）作为超弹性本构人工神经网络（CAN）
Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
AI总结：
本文提出单调输入凸 Kolmogorov-Arnold 网络（ICKAN），通过可训练单调输入凸样条学习物理可接受的多凸超弹性本构模型，在无监督训练下准确捕捉非线性应力-应变行为并具备良好泛化能力。
摘要：
传统本构模型依赖手工设计的参数化形式，其表达能力和泛化能力有限，而基于神经网络的模型能够捕捉复杂材料行为，但往往缺乏可解释性。为了平衡这些权衡，我们提出了单调输入凸 Kolmogorov-Arnold 网络（ICKAN），用于学习多凸超弹性本构定律。ICKAN 利用 Kolmogorov-Arnold 表示，将模型分解为可训练的单变量样条激活函数的组合，以获得丰富的表达能力。我们在 KAN 架构中引入了可训练的单调输入凸样条，确保为各向同性可压缩超弹性提供物理上可接受的多凸模型。所得模型既紧凑又可解释，能够通过单调输入凸符号回归技术显式提取解析本构关系。通过对全场应变数据和有限全局力测量进行无监督训练，ICKAN 能够准确捕捉不同应变状态下的非线性应力-应变行为。使用训练后的 ICKAN 超弹性本构模型对未见几何形状进行有限元模拟，证实了该框架的鲁棒性和泛化能力。
英文摘要：
Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable monotonic input-convex splines within the KAN architecture, ensuring physically admissible polyconvex models for isotropic compressible hyperelasticity. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through a monotonic input-convex symbolic regression technique. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress-strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.
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。
