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Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer…

Machine Learning · Computer Science 2024-12-24 Juan Diego Toscano , Li-Lian Wang , George Em Karniadakis

Constitutive laws relate fluid stress to deformation and underpin predictions of non-Newtonian behavior in industrial and biological fluids. Standard characterization relies on measurements in idealized flows that often miss physics…

The Kolmogorov-Arnold Network (KAN) is a new network architecture known for its high accuracy in several tasks such as function fitting and PDE solving. The superior expressive capability of KAN arises from the Kolmogorov-Arnold…

Machine Learning · Computer Science 2024-12-19 Ruichen Qiu , Yibo Miao , Shiwen Wang , Lijia Yu , Yifan Zhu , Xiao-Shan Gao

Shape Memory Alloys (SMAs) are materials with the ability to recover apparently permanent deformation under specific thermomechanical loading. The majority of constitutive models for SMAs are developed based on the infinitesimal strain…

Materials Science · Physics 2018-12-17 Lei Xu , Theocharis Baxevanis , Dimitris Lagoudas

Inductive Logic Programming (ILP) systems learn generalised, interpretable rules in a data-efficient manner utilising existing background knowledge. However, current ILP systems require training examples to be specified in a structured…

Machine Learning · Computer Science 2021-06-28 Daniel Cunnington , Alessandra Russo , Mark Law , Jorge Lobo , Lance Kaplan

We learn parameterized nonlinear elasticity on curved surfaces using a physics-informed neural network that enforces governing equations and boundary conditions directly through the loss function, enabling a single trained model to…

Biological Physics · Physics 2026-04-15 Yankang Liu , Ke Zhang , Maziar Raissi , Roya Zandi

Kolmogorov-Arnold Networks (KANs) were proposed as an alternative to traditional neural network architectures based on multilayer perceptrons (MLP-NNs). The potential advantages of KANs over MLP-NNs, including significantly enhanced…

Materials Science · Physics 2026-01-29 Ryan Jacobs , Lane E. Schultz , Dane Morgan

Constitutive equations are derived for the time-dependent behavior of particle-reinforced elastomers at isothermal loading with finite strains. A rubbery polymer is modelled as a network of macromolecules bridged by junctions which can slip…

Materials Science · Physics 2007-05-23 Aleksey D. Drozdov , Al Dorfmann

We present the Cholesky-factored symmetric positive definite neural network (SPD-NN) for modeling constitutive relations in dynamical equations. Instead of directly predicting the stress, the SPD-NN trains a neural network to predict the…

Numerical Analysis · Mathematics 2021-02-03 Kailai Xu , Daniel Z. Huang , Eric Darve

This paper proposes a Physics-Informed Kolmogorov-Arnold Network for analyzing elasticity problems in multi-material electronic packaging structures. The method replaces traditional Multi-Layer Perceptrons with Kolmogorov-Arnold Networks…

Numerical Analysis · Mathematics 2026-02-06 Yanpeng Gong , Yida He , Yue Mei , Xiaoying Zhuang , Fei Qin , Timon Rabczuk

This study explores the application of Kolmogorov-Arnold Networks (KANs) in predicting nuclear binding energies, leveraging their ability to decompose complex multi-parameter systems into simpler univariate functions. By utilizing data from…

Nuclear Theory · Physics 2025-02-10 Hao Liu , Jin Lei , Zhongzhou Ren

Kolmogorov-Arnold Networks (KANs) have gained significant attention as an alternative to traditional multilayer perceptrons, with proponents claiming superior interpretability and performance through learnable univariate activation…

Machine Learning · Computer Science 2025-09-16 Yuntian Hou , Tianrui Ji , Di Zhang , Angelos Stefanidis

Physics-informed neural networks provide a mesh-free framework for solving partial differential equation-governed problems in solid mechanics. However, most existing formulations in linear elasticity still learn the displacement field…

Computational Engineering, Finance, and Science · Computer Science 2026-05-05 Shuwei Zhou , Christian Häffner , Sophie Stebner , Niklas Fehlemann , Zhichao Wei , Sebastian Münstermann

Kolmogorov-Arnold Networks (KAN) has recently attracted significant attention as a promising alternative to traditional Multi-Layer Perceptrons (MLP). Despite their theoretical appeal, KAN require validation on large-scale benchmark…

Machine Learning · Computer Science 2024-09-12 Chang Dong , Liangwei Zheng , Weitong Chen

There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional…

Machine Learning · Computer Science 2025-04-16 Raghav Pant , Sikan Li , Xingjian Li , Hassan Iqbal , Krishna Kumar

For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments in stochastic elasticity, we extend…

Soft Condensed Matter · Physics 2020-03-17 L. Angela Mihai , Alain Goriely

Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lam\'e coefficient $\lambda\to\infty$, or equivalently as the Poisson ratio…

Numerical Analysis · Mathematics 2025-10-24 Josef Dick , Seungchan Ko , Quoc Thong Le Gia , Kassem Mustapha , Sanghyeon Park

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides…

Computational Engineering, Finance, and Science · Computer Science 2023-09-07 Shahed Rezaei , Ahmad Moeineddin , Ali Harandi

Deep neural networks achieve state-of-the-art performance in estimating heterogeneous treatment effects, but their opacity limits trust and adoption in sensitive domains such as medicine, economics, and public policy. Building on…

Machine Learning · Statistics 2025-12-08 Alejandro Almodóvar , Patricia A. Apellániz , Santiago Zazo , Juan Parras

While data-driven methods offer significant promise for modeling complex materials, they often face challenges in generalizing across diverse physical scenarios and maintaining physical consistency. To address these limitations, we propose…

Graphics · Computer Science 2025-10-27 Xueguang Xie , Shu Yan , Shiwen Jia , Siyu Yang , Aimin Hao , Yang Gao , Peng Yu