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

  1. M. Azaïez 1
  2. T. Chacón Rebollo 2
  3. M. Gómez Mármol 2
  4. E. Perracchione 3
  5. A. Rincón Casado 4
  6. J. M. Vega 5
  1. 1 University of Bordeaux
    info

    University of Bordeaux

    Burdeos, Francia

    ROR https://ror.org/057qpr032

  2. 2 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

  3. 3 University of Padua
    info

    University of Padua

    Padua, Italia

    ROR https://ror.org/00240q980

  4. 4 Universidad de Cádiz
    info

    Universidad de Cádiz

    Cádiz, España

    ROR https://ror.org/04mxxkb11

  5. 5 Universidad Politécnica de Madrid
    info

    Universidad Politécnica de Madrid

    Madrid, España

    ROR https://ror.org/03n6nwv02

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Journal:
SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada

ISSN: 2281-7875

Year of publication: 2021

Volume: 78

Issue: 2

Pages: 213-232

Type: Article

DOI: 10.1007/S40324-021-00252-3 DIALNET GOOGLE SCHOLAR

More publications in: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada

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Abstract

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.

Data source: Dialnet