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Article Dans Une Revue Mathematics and Mechanics of Complex Systems Année : 2023

An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials

Résumé

An overview of the author works, many of which were carried out in collaboration, is presented. The first part concerns the quantification of uncertainties for complex engineering science systems for which analyzes are now carried out using large numerical simulation models. More recently, machine learning methods have appeared in this field to address certain problems of nonconvex optimization under uncertainties and inverse identification, which are not affordable with standard computer resources. Thus the second part is relative to the presentation of a method of probabilistic learning on manifolds recently proposed for the case of small data and which makes it possible to build statistical surrogate models useful to perform probabilistic inferences. The illustrations are mainly focused on the multiscale analyzes of microstructures made up of heterogeneous continuous materials, which cannot be described in terms of constituents and which are modeled with stochastic apparent quantities at mesoscale.
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Dates et versions

hal-04182250 , version 1 (24-10-2023)

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Christian Soize. An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials. Mathematics and Mechanics of Complex Systems, 2023, 11 (1), pp.87-174. ⟨10.2140/memocs.2023.11.87⟩. ⟨hal-04182250⟩
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