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.

中文翻译：

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KAN 可以吗？输入凸 Kolmogorov-Arnold 网络 （KAN） 作为超弹性本构人工神经网络 （CAN）

传统的本构模型依赖于手工制作的参数形式，具有有限的表达性和泛化性，而基于神经网络的模型可以捕获复杂的材料行为，但往往缺乏可解释性。为了平衡这些权衡，我们提出了用于学习多凸超弹性本构定律的单调输入-凸 Kolmogorov-Arnold 网络 （ICKANs）。ICKAN 利用 Kolmogorov-Arnold 表示，将模型分解为可训练的基于样条的激活函数的组合，以获得丰富的表现力。我们在 KAN 架构中引入了可训练的单调输入凸样条，确保各向同性可压缩超弹性的物理可接受多凸模型。生成的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分析本构关系。通过对全场应变数据和有限的全局力测量进行无监督训练，ICKAN 可以准确捕获不同应变状态下的非线性应力-应变行为。使用经过训练的 ICKAN 超弹性本构模型对看不见的几何结构进行有限元仿真，证实了该框架的稳健性和泛化能力。