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

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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.

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Acknowledgements

This research has been partially supported by the Spanish AEI–Feder Fund, under Grant RTI2018-093521-B-C31 (MA and MGM), Junta de Andalucia-Feder Fund, under Grant US-1254587 (TCR), the European Union Horizon 2020 Program, under the Marie Sklodowska-Curie agreement 872442-ARIA (MA and TCR), ASI-INAF, under Grant AI-FLARES (EP), and the Spanish Ministry of Science, Innovation, and Universities, under Grant TRA2016-75075-R (JMV).

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Authors and Affiliations

  1. Bordeaux INP, I2M (UMR CNRS 5295), Université de Bordeaux, 33607, Pessac, France

    M. Azaïez

  2. Departamento EDAN & IMUS, Universidad de Sevilla, C/Tarfia, s/n, 41012, Seville, Spain

    T. Chacón Rebollo

  3. Departamento EDAN, Universidad de Sevilla, C/Tarfia, s/n, 41012, Seville, Spain

    M. Gómez Mármol

  4. Dipartimento di Matematica, Università degli Studi di Padova, Via Dodecaneso 33, 16146, Genova, Italy

    E. Perracchione

  5. Dpto de Ing. Mecánica y Diseño Industial, Universidad de Cádiz, Avda. Universidad de Cádiz, 10. 11519, Puerto Real, Spain

    A. Rincón Casado

  6. E.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    J. M. Vega

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  1. M. Azaïez
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Azaïez, M., Chacón Rebollo, T., Gómez Mármol, M. et al. Data-driven reduced order modeling based on tensor decompositions and its application to air-wall heat transfer in buildings. SeMA 78, 213–232 (2021). https://doi.org/10.1007/s40324-021-00252-3

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