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arXiv · 2109.08769

Mapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models

Angelo Iollo·Tommaso Taddei
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Abstract

We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to identify the coherent structure we wish to track; a maximum likelihood estimator to identify a Gaussian model of the coherent structure; and a nonlinear interpolation strategy that relies on optimal transportation maps between Gaussian distributions. We show that well-known self-similar solutions can be recast in the frame of optimal transportation by appropriate rescaling; we further present several numerical examples to motivate our proposal and to assess strengths and limitations; finally, we discuss an extension to deal with more complex problems.

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Angelo Iollo, Tommaso Taddei. 2021-09-17. Mapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models. https://doi.org/10.1016/j.jcp.2022.111671

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