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

Mejdi Azaïez; Tomás Chacón Rebollo; Macarena Gómez Mármol; E. Perracchione; Alejandro Rincón Casado; J. Macias

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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
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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
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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.