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Data-driven reduced order modeling based on tensor decompositions and its application to air-wall heat transfer in buildings

  • M. Azaïez [1] ; T. Chacón Rebollo [2] ; M. Gómez Mármol [2] ; E. Perracchione [3] ; A. Rincón Casado [4] ; J. M. Vega [5]
    1. [1] University of Bordeaux

      University of Bordeaux

      Arrondissement de Bordeaux, Francia

    2. [2] Universidad de Sevilla

      Universidad de Sevilla

      Sevilla, España

    3. [3] University of Padua

      University of Padua

      Padova, Italia

    4. [4] Universidad de Cádiz

      Universidad de Cádiz

      Cádiz, España

    5. [5] Universidad Politécnica de Madrid

      Universidad Politécnica de Madrid

      Madrid, España

  • Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 78, Nº. Extra 2, 2021, págs. 213-232
  • Idioma: inglés
  • DOI: 10.1007/s40324-021-00252-3
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • This paper deals with the data-driven reduced order modeling of high dimensional systems, using a tensor decomposition plus one-dimensional interpolation. The (many) involved dimensions are usually associated with space, and/or time, and/or various parameters the system may depend on. Three tensor decomposition methods are considered, namely recursive proper orthogonal decomposition, higher order singular value decomposition, and proper generalized decomposition. The former method exhibits a well-established mathematical foundation (namely, rigorous error estimates have been obtained) in the continuous limit, while rigorous error estimates for the remaining two decompositions are available in the discrete case only. The data-driven ROM is first described and its combination with each of the three tensor decompositions is evaluated using a toy model tensor. In addition, application is made to the real-time simulation of air-wall heat transfer in buildings. In this application, the performance of the data-driven ROM is compared with that of a typical empirical model, as well as with radial basis function interpolation.


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