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Wasserstein model reduction approach for parametrized flow problems in porous media

Abstract : The aim of this work is to build a reduced-order model for parametrized porous media equations. The main challenge of this type of problems is that the Kolmogorov width of the solution manifold typically decays quite slowly and thus makes usual linear model-order reduction methods inappropriate. In this work, we investigate an adaptation of the methodology proposed in [15], based on the use of Wasserstein barycenters [1], to the case of non-conservative problems. Numerical examples in one-dimensional test cases illustrate the advantages and limitations of this approach and suggest further research directions that we intend to explore in the future.
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https://hal.inria.fr/hal-03664061
Contributor : Virginie Ehrlacher Connect in order to contact the contributor
Submitted on : Tuesday, May 10, 2022 - 4:41:15 PM
Last modification on : Wednesday, June 8, 2022 - 12:50:08 PM

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  • HAL Id : hal-03664061, version 1

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Beatrice Battisti, Tobias Blickhan, Guillaume Enchery, Virginie Ehrlacher, Damiano Lombardi, et al.. Wasserstein model reduction approach for parametrized flow problems in porous media. 2022. ⟨hal-03664061⟩

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