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Surrogate parametric metamodel based on Optimal Transport

Article dans une revue avec comité de lecture
Author
TORREGROSA, Sergio
CHAMPANEY, Victor
ccAMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
HERBERT, Vincent
1086610 Stellantis France
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/22204
DOI
10.1016/j.matcom.2021.11.010
Date
2021-11-30
Journal
Mathematics and Computers in Simulation

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.

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