Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)

Abstract

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.

36 pages, 16 figures

References in corpus (23)

• KAN: Kolmogorov-Arnold Networks
• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
• NN-EUCLID: deep-learning hyperelasticity without stress data
• Neural networks meet hyperelasticity: A guide to enforcing physics
• Automated discovery of generalized standard material models with EUCLID
• Data-driven fracture mechanics
• Discovering plasticity models without stress data
• Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations
• Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks
• Finite electro-elasticity with physics-augmented neural networks
• Automated identification of linear viscoelastic constitutive laws with EUCLID
• Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID
• On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning
• Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions
• Physics-informed Data-driven Discovery of Constitutive Models with Application to Strain-Rate-sensitive Soft Materials
• Automated Data-Driven Discovery of Material Models Based on Symbolic Regression: A Case Study on Human Brain Cortex
• HyperCAN: Hypernetwork-Driven Deep Parameterized Constitutive Models for Metamaterials
• Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues
• Experimental Learning of a Hyperelastic Behavior with a Physics-Augmented Neural Network
• Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KAN
• KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
• Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

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