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Empowering optimal transport matching algorithm for the construction of surrogate parametric metamodel

Article dans une revue avec comité de lecture
Author
ccJACOT, Maurine
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
505477 Safran Tech
CHAMPANEY, Victor
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
ccTORREGROSA JORDAN, Sergio
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
ccCORTIAL, Julien
505477 Safran Tech
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
1166977 CNRS@CREATE Ltd.

URI
http://hdl.handle.net/10985/25778
DOI
10.1051/meca/2024001
Date
2024-03
Journal
Mechanics & Industry

Abstract

Resolving Partial Differential Equations (PDEs) through numerical discretization methods like the Finite Element Method presents persistent challenges associated with computational complexity, despite achieving a satisfactory solution approximation. To surmount these computational hurdles, interpolation techniques are employed to precompute models offline, facilitating rapid online solutions within a metamodel. Probability distribution frameworks play a crucial role in data modeling across various fields such as physics, statistics, and machine learning. Optimal Transport (OT) has emerged as a robust approach for probability distribution interpolation due to its ability to account for spatial dependencies and continuity. However, interpolating in high-dimensional spaces encounters challenges stemming from the curse of dimensionality. The article offers insights into the application of OT, addressing associated challenges and proposing a novel methodology. This approach utilizes the distinctive arrangement of an ANOVA-based sampling to interpolate between more than two distributions using a step-by-step matching algorithm. Subsequently, the ANOVA-PGD method is employed to construct the metamodel, providing a comprehensive solution to address the complexities inherent in distribution interpolation.

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