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

• URL: http://arxiv.org/abs/2503.05617v1
• Date: Fri, 07 Mar 2025 17:42:24 GMT
• Title: Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
• Authors: Prakash Thakolkaran, Yaqi Guo, Shivam Saini, Mathias Peirlinck, Benjamin Alheit, Siddhant Kumar,
• Abstract summary: We present ICKANs (ICKANs) for learning poly inputelastic laws.<n>The resulting models are enabling explicit extraction of analytical relationships.<n>We show that ICKANs accurately capture strain stress-strain behavior across diverse states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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 input-convex splines within the KAN architecture, ensuring physically admissible polyconvex hyperelastic models. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through an input-convex symbolic regression techinque. 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.

Related papers

• EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials [0.0]
  We present an elasto-plasticity informed Chebyshev-based network (EPi-cKAN) EPi-cKAN provides superior accuracy in predicting stress components and demonstrates better accuracy when used to predict sand elasto-plastic behavior under blind triaxial axisymmetric strain-controlled loading paths.
  arXiv  Detail & Related papers  (2024-10-12T16:01:38Z)
• Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations [56.78271181959529]
  Generalized Additive Models (GAMs) can capture non-linear relationships between variables and targets, but they cannot capture intricate feature interactions. We propose Shape Expressions Arithmetic ( SHAREs) that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints.
  arXiv  Detail & Related papers  (2024-04-15T13:44:01Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics [0.0]
  We propose to train regularized physics-augmented neural network-based models utilizing a smoothed version of $L0$-regularization. We show that the method can reliably obtain interpretable and trustworthy models for compressible and incompressible thermodynamicity, yield functions, and hardening models for elastoplasticity.
  arXiv  Detail & Related papers  (2023-10-05T16:28:58Z)
• On the Trade-off Between Efficiency and Precision of Neural Abstraction [62.046646433536104]
  Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. We employ formal inductive synthesis procedures to generate neural abstractions that result in dynamical models with these semantics.
  arXiv  Detail & Related papers  (2023-07-28T13:22:32Z)
• Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction [45.84205238554709]
  We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. We include the Gibbs-Duhem equation explicitly in the loss function for training neural networks.
  arXiv  Detail & Related papers  (2023-05-31T07:36:45Z)
• Viscoelastic Constitutive Artificial Neural Networks (vCANNs) $-$ a framework for data-driven anisotropic nonlinear finite viscoelasticity [0.0]
  We introduce viscoelastic Constitutive Artificial Neural Networks (vCANNs) vCANNs are a novel physics-informed machine learning framework for anisotropic nonlinear viscoity at finite strains. We demonstrate that vCANNs can learn to capture the behavior of all these materials accurately and efficiently without human guidance.
  arXiv  Detail & Related papers  (2023-03-21T19:45:59Z)
• NN-EUCLID: deep-learning hyperelasticity without stress data [0.0]
  We propose a new approach for unsupervised learning of hyperelastic laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the stress-strain, the approach only uses realistically measurable full-elastic field displacement and global force availability data.
  arXiv  Detail & Related papers  (2022-05-04T13:54:54Z)
• EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
  We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting. We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
  arXiv  Detail & Related papers  (2022-02-21T18:59:03Z)
• MD-inferred neural network monoclinic finite-strain hyperelasticity models for $\beta$-HMX: Sobolev training and validation against physical constraints [2.3816618027381438]
  We train and validate neural networks to predict the anisotropic elastic response of the monoclinic organic molecular crystal $beta$-HMX. We compare the neural networks' training efficiency under different Sobolev constraints and assess the models' accuracy and robustness against MD benchmarks for $beta$-HMX.
  arXiv  Detail & Related papers  (2021-11-29T23:38:31Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Hyperbolic Neural Networks++ [66.16106727715061]
  We generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar'e ball model. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.
  arXiv  Detail & Related papers  (2020-06-15T08:23:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.