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Optimal Upscaling with Transport Maps


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dc.contributorChinedu Eleh, nedueleh@gmail.comen_US
dc.creatorEleh, Chinedu
dc.creatorvan Wyk, Hans-Werner
dc.date.accessioned2024-04-04T15:00:44Z
dc.date.available2024-04-04T15:00:44Z
dc.date.created2022-06-16
dc.identifier.urihttps://aurora.auburn.edu/handle/11200/50637
dc.identifier.urihttp://dx.doi.org/10.35099/aurora-705
dc.description.abstractPartial differential equation models often involve space-dependent parameters, such as diffusion coefficients and advection fields, that cannot be measured explicitly and are therefore uncertain. Midpoint (MP), spatial averaging (SA), shape function (SF) and series expansion (SE) methods have long existed in the stochastic simulation community and are well known for their computational hurdles. In this work, we compute efficient, spatially adaptive, lower-dimensional approximations of these fields, using transport maps. Such parsimonious representations of the parameter space would greatly improve the efficiency of the resulting stochastic simulations, allow for more targeted use of reduced order models, and aid in the related design of interventions. Numerical examples demonstrate our theoretical resultsen_US
dc.formatPDFen_US
dc.publisherSimons Laufer Mathematical Sciences Instituteen_US
dc.relation.ispartofIntegral Equations and Applicationsen_US
dc.rightsCC BY 4.0en_US
dc.subjectTransport Maps, Upscalingen_US
dc.titleOptimal Upscaling with Transport Mapsen_US
dc.typeTexten_US
dc.type.genrePresentation, Poster Presentationen_US
dc.locationBerkeley, CAen_US

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