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A Data-Driven ROM Based on HODMD

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14th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2019) (SOCO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 950))

Abstract

A preliminary version of a data driven reduced order model (ROM) for dynamical systems is presented in this Chapter. This ROM synergically and adaptively combines a black-box full model (FM) of the system and extrapolate conveniently using a recent extension of standard dynamic mode decomposition called higher order dynamic mode decomposition (HODMD). These two are applied in interspersed time intervals, called the FM-intervals and the HODMD-intervals, respectively. The data for the each HODMD-interval is obtained from the application of the FM in the previous FM-interval. The main question is when extrapolation from HODMD is no longer valid and switching to a new FM-interval is necessary. This is made attending to two criteria, ensuring that an estimate of the extrapolation error and a measure of consistency are both conveniently small. In this sense, the present method is similar to a previous method called POD on the Fly, which was not a purely data driven method. Instead, POD on the Fly was based on a Galerkin projection of the governing equations that thus should be known. The new method presented in this paper is illustrated with several transient dynamics for the complex Ginzburg-Landau equation that converges to either periodic or quasi-periodic attractors. The resulting CPU accelerations factors (compared to the full model) are quite large.

Supported by the Spanish Ministry of Economy and Competitiveness, under Grant TRA-2016-75075-R.

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Acknowledgements

This research has been supported by the Spanish Ministry of Economy and Competitiveness, under grant TRA2016-75075-R.

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Authors and Affiliations

  1. School of Aerospace Engineering, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    Víctor Beltrán, Soledad Le Clainche & José M. Vega

Authors
  1. Víctor Beltrán
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  2. Soledad Le Clainche
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  3. José M. Vega
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Corresponding author

Correspondence to José M. Vega .

Editor information

Editors and Affiliations

  1. Data Science and Big Data Lab, Pablo de Olavide University, Seville, Spain

    Francisco Martínez Álvarez

  2. Data Science and Big Data Lab, Pablo de Olavide University, Seville, Spain

    Alicia Troncoso Lora

  3. University of Salamanca, Salamanca, Spain

    José António Sáez Muñoz

  4. Department of Industrial Engineering, University of A Coruña, A Coruña, Spain

    Héctor Quintián

  5. University of Salamanca, Salamanca, Spain

    Emilio Corchado

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Beltrán, V., Clainche, S.L., Vega, J.M. (2020). A Data-Driven ROM Based on HODMD. In: Martínez Álvarez, F., Troncoso Lora, A., Sáez Muñoz, J., Quintián, H., Corchado, E. (eds) 14th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2019). SOCO 2019. Advances in Intelligent Systems and Computing, vol 950. Springer, Cham. https://doi.org/10.1007/978-3-030-20055-8_54

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