  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.
