Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models
arXiv:2602.17750v1 Announce Type: cross 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 proc
arXiv:2602.17750v1 Announce Type: cross 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.
Executive Summary
The article introduces inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs), a novel artificial neural network architecture designed to automate the discovery of symbolic constitutive laws for materials. These laws describe the relationship between strain and stress, encompassing both elastic and inelastic behaviors. The study demonstrates the efficacy of iCKANs using synthetic data and experimental data from viscoelastic polymers VHB 4910 and VHB 4905. The results highlight the ability of iCKANs to accurately capture complex viscoelastic behaviors while maintaining physical interpretability. Additionally, iCKANs can process supplementary information, such as temperature-dependent behavior, making them a versatile tool for future material property discoveries under various conditions.
Key Points
- ▸ iCKANs automate the discovery of symbolic constitutive laws for materials.
- ▸ They accurately capture complex viscoelastic behaviors while preserving interpretability.
- ▸ iCKANs can process additional information like temperature-dependent behavior.
Merits
Automated Discovery
iCKANs automate the process of discovering constitutive laws, which traditionally requires significant manual effort and expertise.
Interpretability
The networks produce symbolic constitutive laws that are physically interpretable, making them valuable for practical applications.
Versatility
iCKANs can process a wide range of data, including mechanical data and additional information like temperature-dependent behavior.
Demerits
Data Dependency
The effectiveness of iCKANs is highly dependent on the quality and quantity of the input data, which may limit their applicability in scenarios with limited data.
Complexity
The complexity of the neural network architecture may require significant computational resources and expertise to implement and interpret.
Validation
The study primarily uses synthetic and specific experimental data, and further validation with a broader range of materials and conditions is necessary.
Expert Commentary
The introduction of iCKANs represents a significant advancement in the field of material science, particularly in the automated discovery of constitutive laws. The ability to translate complex material testing data into interpretable symbolic laws is a notable achievement, as it bridges the gap between data-driven approaches and traditional material modeling. The study's demonstration using both synthetic and experimental data lends credibility to the method, although further validation with a diverse set of materials and conditions would strengthen its applicability. The versatility of iCKANs in processing additional information, such as temperature-dependent behavior, underscores their potential for future research. However, the dependency on high-quality data and the complexity of the neural network architecture present challenges that need to be addressed. Overall, iCKANs hold promise for accelerating material discovery and improving the accuracy of material property predictions, which could have profound implications for various industries and policy frameworks.
Recommendations
- ✓ Conduct further validation studies with a broader range of materials and experimental conditions to establish the robustness of iCKANs.
- ✓ Explore the integration of iCKANs with other machine learning techniques to enhance their predictive capabilities and interpretability.
