Speaker
Description
Hybrid constitutive modeling combines two complementary approaches for describing and predicting a material’s mechanical behavior: data-driven black-box methods and physically constrained, theory-based models [1,2]. While black-box methods can achieve high accuracy, they often lack interpretability and extrapolation capabilities. In contrast, physics-based models offer theoretical insight and generalizability but may struggle to capture complex behaviors with the same precision. Traditionally, hybrid modeling has required a compromise between these strengths.
In this presentation, we demonstrate how recent advancements in symbolic machine learning—particularly Kolmogorov-Arnold Networks (KANs)—help mitigate this trade-off. We present Constitutive Kolmogorov-Arnold Networks (CKANs) [3] as a novel class of hybrid constitutive models. By integrating a post-processing symbolification step, CKANs retain the predictive accuracy of data-driven models while enhancing interpretability and extrapolation through symbolic expressions, effectively bridging machine learning and physical modeling.
References:
[1] K. Linka, M. Hillgärtner, K.P. Abdolazizi, R.C. Aydin, M. Itskov, C.J. Cyron, Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning, Journal of Computational Physics, 429:110010, 2021.
[2] K.P. Abdolazizi, K. Linka, C.J. Cyron, Viscoelastic constitutive artificial neural networks (vCANNs) - A framework for data-driven anisotropic nonlinear finite viscoelasticity, Journal of Computational Physics, 499:112704, 2024.
[3] K.P. Abdolazizi, R.C. Aydin, C.J. Cyron, K. Linka, Constitutive Kolmogorov–Arnold Networks (CKANs): Combining Accuracy and Interpretability in Data-Driven Material Modeling, Preprint, https://arxiv.org/abs/2502.05682, 2025.
