Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation

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Open AccessArticle
Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation
by Sergio Torregrosa 1,2,*ORCID,David Muñoz 1,Vincent Herbert 2 andFrancisco Chinesta 1
1
PIMM Laboratory, Arts et Métiers Institute of Technology, 151 Boulevard de l’Hopital, 75013 Paris, France
2
STELLANTIS, 10 Boulevard de l’Europe, 78300 Poissy, France
*
Author to whom correspondence should be addressed.
Technologies 2024, 12(2), 20; https://doi.org/10.3390/technologies12020020
Submission received: 20 November 2023 / Revised: 18 January 2024 / Accepted: 22 January 2024 / Published: 2 February 2024
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Abstract
When training a parametric surrogate to represent a real-world complex system in real time, there is a common assumption that the values of the parameters defining the system are known with absolute confidence. Consequently, during the training process, our focus is directed exclusively towards optimizing the accuracy of the surrogate’s output. However, real physics is characterized by increased complexity and unpredictability. Notably, a certain degree of uncertainty may exist in determining the system’s parameters. Therefore, in this paper, we account for the propagation of these uncertainties through the surrogate using a standard Monte Carlo methodology. Subsequently, we propose a novel regression technique based on optimal transport to infer the impact of the uncertainty of the surrogate’s input on its output precision in real time. The OT-based regression allows for the inference of fields emulating physical reality more accurately than classical regression techniques, including advanced ones.