Regular Article

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

¹ PIMM Lab, Arts et Métiers Institute of Technology, 155 Boulevard de l’Hôpital, 75013 Paris, France
² Safran Tech, Department of Digital Sciences and Technologies,1 rue des Jeunes Bois, 78117, Châteaufort, France
³ CNRS@CREATE LTD, 1 Create Way, # 08-01 CREATE Tower, 138602 Singapore

^* e-mail: maurine.jacot@ensam.eu

Received: 10 August 2023
Accepted: 10 January 2024

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.