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Surrogate parametric metamodel based on Optimal Transport

Author

Listed:
  • Torregrosa, Sergio
  • Champaney, Victor
  • Ammar, Amine
  • Herbert, Vincent
  • Chinesta, Francisco

Abstract

The description of a physical problem through a model necessarily involves the introduction of parameters. Hence, one wishes to have a solution of the problem that is a function of all these parameters: a parametric solution. However, the construction of such parametric solutions exhibiting localization in space is only ensured by costly and time-consuming tests, which can be both numerical or experimental. Numerical methodologies used classically imply enormous computational efforts for exploring the design space. Therefore, parametric solutions obtained using advanced nonlinear regressions are an essential tool to address this challenge. However, classical regression techniques, even the most advanced ones, can lead to non physical interpolation in some fields such as fluid dynamics, where the solution localizes in different regions depending on the problem parameters choice. In this context, Optimal Transport (OT) offers a mathematical approach to measure distances and interpolate between general objects in a, sometimes, more physical way than the classical interpolation approach. Thus, OT has become fundamental in some fields such as statistics or computer vision, and it is being increasingly used in fields such as computational mechanics. However, the OT problem is usually computationally costly to solve and not adapted to be accessed in an online manner. Therefore, the aim of this paper is combining advanced nonlinear regressions with Optimal Transport in order to implement a parametric real-time model based on OT. To this purpose, a parametric model is built offline relying on Model Order Reduction and OT, leading to a real-time interpolation tool following Optimal Transport theory. Such a tool is of major interest in design processes, but also within the digital twin rationale.

Suggested Citation

  • Torregrosa, Sergio & Champaney, Victor & Ammar, Amine & Herbert, Vincent & Chinesta, Francisco, 2022. "Surrogate parametric metamodel based on Optimal Transport," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 36-63.
  • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:36-63
    DOI: 10.1016/j.matcom.2021.11.010
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    Citations

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    Cited by:

    1. Delagnes, T. & Henneron, T. & Clenet, S. & Fratila, M. & Ducreux, J.P., 2023. "Comparison of reduced basis construction methods for Model Order Reduction, with application to non-linear low frequency electromagnetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 470-488.
    2. Chady Ghnatios & Xavier Kestelyn & Guillaume Denis & Victor Champaney & Francisco Chinesta, 2023. "Learning Data-Driven Stable Corrections of Dynamical Systems—Application to the Simulation of the Top-Oil Temperature Evolution of a Power Transformer," Energies, MDPI, vol. 16(15), pages 1-21, August.

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