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A Manifold Learning Approach to Data-Driven Computational Elasticity and Inelasticity

  • S.I.: Machine learning in computational mechanics
  • Published:
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Abstract

Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,...), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Even if one can be confident on the first type of equations, the second one contains modeling errors. Moreover, this second type of equations remains too particular and often fails in describing new experimental results. The vast majority of existing models lack of generality, and therefore must be constantly adapted or enriched to describe new experimental findings. In this work we propose a new method, able to directly link data to computers in order to perform numerical simulations. These simulations will employ axiomatic, universal laws while minimizing the need of explicit, often phenomenological, models. This technique is based on the use of manifold learning methodologies, that allow to extract the relevant information from large experimental datasets.

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Acknowledgments

This work has been supported by ESI GROUP through the ECN-ESI Chair on advanced modeling and simulation of materials, structures and processes as well as by the Spanish Ministry of Economy and Competitiveness through Grants Number CICYT DPI2014-51844-C2-1-R and DPI2015-72365-EXP and by the Regional Government of Aragon and the European Social Fund, Research Group T88.

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Authors and Affiliations

  1. High Performance Computing Institute and ESI GROUP Chair, Ecole Centrale de Nantes, 1 Rue de la Noe, 44300, Nantes, France

    Rubén Ibañez, Emmanuelle Abisset-Chavanne, Jose Vicente Aguado & Francisco Chinesta

  2. Aragon Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain

    David Gonzalez & Elias Cueto

Authors
  1. Rubén Ibañez
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  2. Emmanuelle Abisset-Chavanne
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  3. Jose Vicente Aguado
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  4. David Gonzalez
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  5. Elias Cueto
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  6. Francisco Chinesta
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Corresponding author

Correspondence to Francisco Chinesta.

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The research does not involve neither human participants nor animals

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Ibañez, R., Abisset-Chavanne, E., Aguado, J.V. et al. A Manifold Learning Approach to Data-Driven Computational Elasticity and Inelasticity. Arch Computat Methods Eng 25, 47–57 (2018). https://doi.org/10.1007/s11831-016-9197-9

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  • DOI: https://doi.org/10.1007/s11831-016-9197-9

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