Constitutive Kolmogorov-Arnold Networks (CKANs): Combining Accuracy and Interpretability in Data-Driven Material Modeling

TL;DR

This paper introduces CKANs, a hybrid modeling approach that combines the accuracy of data-driven methods with the interpretability of symbolic expressions, advancing material modeling techniques.

Contribution

The paper presents CKANs, a novel class of models that integrate Kolmogorov-Arnold Networks with symbolic post-processing for improved interpretability and extrapolation.

Findings

CKANs achieve high predictive accuracy.

CKANs provide interpretable symbolic expressions.

CKANs outperform traditional hybrid models.

Abstract

Hybrid constitutive modeling integrates two complementary approaches for describing and predicting a material's mechanical behavior: purely data-driven black-box methods and physically constrained, theory-based models. While black-box methods offer high accuracy, they often lack interpretability and extrapolability. Conversely, physics-based models provide theoretical insight and generalizability but may not capture complex behaviors with the same accuracy. Traditionally, hybrid modeling has required a trade-off between these aspects. In this paper, we show how recent advances in symbolic machine learning, specifically Kolmogorov-Arnold Networks (KANs), help to overcome this limitation. We introduce Constitutive Kolmogorov-Arnold Networks (CKANs) as a new class of hybrid constitutive models. By incorporating a post-processing symbolification step, CKANs combine the predictive accuracy of data-driven models with the interpretability and extrapolation capabilities of symbolic expressions, bridging the gap between machine learning and physical modeling.