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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.05682 |
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| _version_ | 1866910847293456384 |
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| author | Abdolazizi, Kian P. Aydin, Roland C. Cyron, Christian J. Linka, Kevin |
| author_facet | Abdolazizi, Kian P. Aydin, Roland C. Cyron, Christian J. Linka, Kevin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constitutive Kolmogorov-Arnold Networks (CKANs): Combining Accuracy and Interpretability in Data-Driven Material Modeling Abdolazizi, Kian P. Aydin, Roland C. Cyron, Christian J. Linka, Kevin Computational Physics Materials Science 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. |
| title | Constitutive Kolmogorov-Arnold Networks (CKANs): Combining Accuracy and Interpretability in Data-Driven Material Modeling |
| topic | Computational Physics Materials Science |
| url | https://arxiv.org/abs/2502.05682 |