A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues
We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the p...
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MDPI AG
2020-05-01
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| Online Access: | https://www.mdpi.com/1996-1944/13/10/2319 |
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| author | David González Alberto García-González Francisco Chinesta Elías Cueto |
| author_facet | David González Alberto García-González Francisco Chinesta Elías Cueto |
| author_sort | David González |
| collection | DOAJ |
| description | We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach. |
| first_indexed | 2024-03-10T19:45:43Z |
| format | Article |
| id | doaj.art-61a6cee85cf94b12a88ab1c79b40705f |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T19:45:43Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-61a6cee85cf94b12a88ab1c79b40705f2023-11-20T00:51:32ZengMDPI AGMaterials1996-19442020-05-011310231910.3390/ma13102319A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft TissuesDavid González0Alberto García-González1Francisco Chinesta2Elías Cueto3Aragon Institute of Engineering Research, Universidad de Zaragoza, 50018 Zaragoza, SpainLaboratori de Càlcul Numèric, E.T.S. de Ingeniería de Caminos, Universitat Politècnica de Catalunya, 08034 Barcelona, SpainESI Group Chair, Processes and Engineering in Mechanics and Materials (PIMM) Laboratory, Arts et Metiers Institute of Technology, 75013 Paris, FranceAragon Institute of Engineering Research, Universidad de Zaragoza, 50018 Zaragoza, SpainWe address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach.https://www.mdpi.com/1996-1944/13/10/2319machine learningmanifold learningtopological data analysisGENERICsoft living tissueshyperelasticity |
| spellingShingle | David González Alberto García-González Francisco Chinesta Elías Cueto A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues Materials machine learning manifold learning topological data analysis GENERIC soft living tissues hyperelasticity |
| title | A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues |
| title_full | A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues |
| title_fullStr | A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues |
| title_full_unstemmed | A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues |
| title_short | A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues |
| title_sort | data driven learning method for constitutive modeling application to vascular hyperelastic soft tissues |
| topic | machine learning manifold learning topological data analysis GENERIC soft living tissues hyperelasticity |
| url | https://www.mdpi.com/1996-1944/13/10/2319 |
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