Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

2026-02-19

AI Summary

This work addresses the challenge of automatically discovering constitutive models from material testing data that are both highly accurate and physically interpretable. The authors propose iCKAN, a novel neural network architecture that uniquely integrates Kolmogorov–Arnold networks with symbolic regression to directly learn closed-form expressions for elastic and inelastic potential functions from experimental data. The framework further supports the incorporation of multi-source physical information, such as temperature dependence. Validated on both synthetic datasets and experimental data from VHB 4910/4905 polymers, iCKAN accurately captures complex viscoelastic behaviors and successfully generates constitutive equations with clear physical meaning, thereby achieving a unified balance between predictive accuracy and interpretability.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.

Problem

• constitutive law
• inelastic behavior
• material modeling
• viscoelasticity
• interpretable machine learning

Innovation

• inelastic constitutive modeling
• Kolmogorov-Arnold Networks
• interpretable machine learning
• viscoelastic materials
• symbolic discovery