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Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction

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Abstract

Compressed sensing is a signal compression technique with very remarkable properties. Among them, maybe the most salient one is its ability of overcoming the Shannon–Nyquist sampling theorem. In other words, it is able to reconstruct a signal at less than 2Q samplings per second, where Q stands for the highest frequency content of the signal. This property has, however, important applications in the field of computational mechanics, as we analyze in this paper. We consider a wide variety of applications, such as model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. Examples are provided for all of them that show the potentialities of compressed sensing in terms of CPU savings in the field of computational mechanics.

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Acknowledgements

This work has been supported by the Spanish Ministry of Economy and Competitiveness through Grants Numbers DPI2017-85139-C2-1-R and DPI2015-72365-EXP and by the Regional Government of Aragon and the European Social Fund, research group T24 17R. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 675919.

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Authors and Affiliations

  1. ESI Group Chair, Ecole Centrale de Nantes, Nantes, France

    R. Ibañez

  2. ESI Chair and I2M Lab, Arts et Métiers ParisTech Centre de Bordeaux-Talence, Esplanade des Arts et Métiers, 33400, Talence, France

    E. Abisset-Chavanne

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

    E. Cueto

  4. LAMPA, ENSAM Angers, 2 Boulevard du Ronceray, BP 93525, 49035, Angers Cedex 01, France

    A. Ammar

  5. ESI Group, 3bis rue Saarinen, 94528, Rungis CEDEX, France

    J. -L. Duval

  6. ESI Chair at PIMM Lab, ENSAM ParisTech, Paris, France

    F. Chinesta

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  1. R. Ibañez
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Correspondence to E. Cueto.

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Ibañez, R., Abisset-Chavanne, E., Cueto, E. et al. Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction. Comput Mech 64, 1259–1271 (2019). https://doi.org/10.1007/s00466-019-01703-5

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