A data-driven method for modeling creep–fatigue stress–strain behavior using neural ODEs.
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| Title: | A data-driven method for modeling creep–fatigue stress–strain behavior using neural ODEs. |
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| Authors: | Deng, Hao1 (AUTHOR) haodeng677@gmail.com, Messner, Mark C.1 (AUTHOR) |
| Source: | Optimization & Engineering. Mar2026, Vol. 27 Issue 1, p617-650. 34p. |
| Subjects: | Stress-strain curves, Artificial neural networks, Strains & stresses (Mechanics), Machine learning, Statistical models, Nonlinear systems, Nickel alloys |
| Abstract: | In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke's Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model's accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form. [ABSTRACT FROM AUTHOR] |
| Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 191979003 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A data-driven method for modeling creep–fatigue stress–strain behavior using neural ODEs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Deng%2C+Hao%22">Deng, Hao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> haodeng677@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Messner%2C+Mark+C%2E%22">Messner, Mark C.</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Optimization+%26+Engineering%22">Optimization & Engineering</searchLink>. Mar2026, Vol. 27 Issue 1, p617-650. 34p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stress-strain+curves%22">Stress-strain curves</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Nickel+alloys%22">Nickel alloys</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke's Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model's accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11081-025-10028-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 34 StartPage: 617 Subjects: – SubjectFull: Stress-strain curves Type: general – SubjectFull: Artificial neural networks Type: general – SubjectFull: Strains & stresses (Mechanics) Type: general – SubjectFull: Machine learning Type: general – SubjectFull: Statistical models Type: general – SubjectFull: Nonlinear systems Type: general – SubjectFull: Nickel alloys Type: general Titles: – TitleFull: A data-driven method for modeling creep–fatigue stress–strain behavior using neural ODEs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Deng, Hao – PersonEntity: Name: NameFull: Messner, Mark C. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13894420 Numbering: – Type: volume Value: 27 – Type: issue Value: 1 Titles: – TitleFull: Optimization & Engineering Type: main |
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