Abdolazizi, Kian PhilippKian PhilippAbdolaziziAydin, RolandRolandAydinCyron, Christian J.Christian J.CyronLinka, KevinKevinLinka2025-07-092025-07-092025-10-01Journal of the Mechanics and Physics of Solids 203: 106212 (2025)https://hdl.handle.net/11420/56130Hybrid 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.en1873-47822025Elsevierhttps://creativecommons.org/licenses/by/4.0/Constitutive Artificial Neural NetworksData-driven mechanicsInterpretable machine learningKolmogorov–Arnold NetworksPhysics-informed machine learningSoft materialsSymbolic regressionTechnology::620: Engineering::620.1: Engineering Mechanics and Materials ScienceComputer Science, Information and General Works::006: Special computer methods::006.3: Artificial IntelligenceJournal Articlehttps://doi.org/10.15480/882.1535710.1016/j.jmps.2025.10621210.15480/882.15357Journal Article