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

Angelo Iollo (1, 2) , Tommaso Taddei (1, 2)

1 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
2 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Analyse numérique [math.NA]

Angelo Iollo, Tommaso Taddei. Mapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models. Journal of Computational Physics, 2022, 471 (111671), pp.111671. ⟨10.1016/j.jcp.2022.111671⟩. ⟨hal-03441730v2⟩